SAT: Geometry & Trig - Area and Volume

Posljednje ažuriranje 4 months ago

SAT: Geometry & Trig - Area and Volume

Posljednje ažuriranje 4 months ago

The length of each edge of a box is $29$ inches. Each side of the box is in the shape of a square. The box does not have a lid. What is the exterior surface area, in square inches, of this box without a lid?

A right circular cylinder has a volume of $45\pi$. If the height of the cylinder is $5$, what is the radius of the cylinder?

$3$

$4.5$

$9$

$40$

Square A has side lengths that are $16$ times the side lengths of square B. The area of square A is $k$ times the area of square B. What is the value of $k$?

What is the area, in square inches, of a rectangle with a length of 7 inches and a width of 6 inches?

The side length of a square is 55 centimeters (cm). What is the area, in $\text{cm}^2$, of the square?

110

220

3,025

12,100

Triangle R has an area of 80 square centimeters ($\text{cm}^2$). Square S has side lengths of 4 cm. What is the total area of triangle R and square S, in $\text{cm}^2$?

What is the length of one side of a square that has the same area as a circle with radius $2$?

$2$

$\sqrt{2\pi}$

$2\sqrt{\pi}$

$2\pi$

A right square prism has a height of 14 units. The volume of the prism is $2{,}016$ cubic units. What is the length, in units, of an edge of the base?

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

The circumference of the base of a right circular cylinder is $20\pi$ meters, and the height of the cylinder is 6 meters. What is the volume, in cubic meters, of the cylinder?

$60\pi$

$120\pi$

$600\pi$

$2,400\pi$

Note: Figure not drawn to scale.
In the figure shown, triangle $JKL$ is similar to triangle $RST$, where $J$ corresponds to $R$ and $K$ corresponds to $S$. The length of $\overline{JK}$ is $15$, and the perimeter of triangle $JKL$ is $36$. The length of $\overline{RS}$ is $135$. What is the perimeter of triangle $RST$?

$324$

$540$

$2{,}916$

$8{,}100$

The area of a square is 64 square inches. What is the side length, in inches, of this square?

128

A circle has a radius of 43 meters. What is the area, in square meters, of the circle?

$\dfrac{43\pi}{2}$

$43\pi$

$86\pi$

$1{,}849\pi$

The three points shown define a circle. The circumference of this circle is $k\pi$, where $k$ is a constant. What is the value of $k$?

Question: What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?

A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

149,796

164,500

190,955

310,800

A right rectangular prism has a length of 11 meters, a width of 8 meters, and a height of 10 meters. What is the volume, in cubic meters, of the prism?

The figure shown is a right circular cylinder with a radius of $r$ and height of $h$. A second right circular cylinder (not shown) has a volume that is 392 times as large as the volume of the cylinder shown. Which of the following could represent the radius $R$, in terms of $r$, and the height $H$, in terms of $h$, of the second cylinder?

$R = 8r$ and $H = 7h$

$R = 8r$ and $H = 49h$

$R = 7r$ and $H = 8h$

$R = 49r$ and $H = 8h$

A right circular cylinder has a volume of $377$ cubic centimeters. The area of the base of the cylinder is $13$ square centimeters. What is the height, in centimeters, of the cylinder?

The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?

A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?

164

1,681

10,086

68,921

The length of the edge of the base of a right square prism is 6 units. The volume of the prism is 2,880 cubic units. What is the height, in units, of the prism?

$4\sqrt{30}$

$24\sqrt{5}$

A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

$16\pi$

$96\pi$

$192\pi$

$768\pi$

The length of each edge of a box is $29$ inches. Each side of the box is in the shape of a square. The box does not have a lid. What is the exterior surface area, in square inches, of this box without a lid?

A right circular cylinder has a volume of $45\pi$. If the height of the cylinder is 5, what is the radius of the cylinder?

4.5

Square A has side lengths that are $16$ times the side lengths of square B. The area of square A is $k$ times the area of square B. What is the value of $k$?

What is the area, in square inches, of a rectangle with a length of 7 inches and a width of 6 inches?

The side length of a square is 55 centimeters (cm). What is the area, in $\text{cm}^2$, of the square?

110

220

3,025

12,100

Triangle R has an area of 80 square centimeters ($\text{cm}^2$). Square S has side lengths of 4 cm. What is the total area of triangle R and square S, in $\text{cm}^2$?

What is the length of one side of a square that has the same area as a circle with radius $2$?

$2$

$\sqrt{2\pi}$

$2\sqrt{\pi}$

$2\pi$

A right square prism has a height of 14 units. The volume of the prism is $2{,}016$ cubic units. What is the length, in units, of an edge of the base?

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

The circumference of the base of a right circular cylinder is $20\pi$ meters, and the height of the cylinder is 6 meters. What is the volume, in cubic meters, of the cylinder?

$60\pi$

$120\pi$

$600\pi$

$2{,}400\pi$

Note: Figure not drawn to scale.
In the figure shown, triangle $JKL$ is similar to triangle $RST$, where $J$ corresponds to $R$ and $K$ corresponds to $S$. The length of $\overline{JK}$ is $15$, and the perimeter of triangle $JKL$ is $36$. The length of $\overline{RS}$ is $135$. What is the perimeter of triangle $RST$?

$324$

$540$

$2{,}916$

$8{,}100$

The area of a square is 64 square inches. What is the side length, in inches, of this square?

128

A circle has a radius of 43 meters. What is the area, in square meters, of the circle?

$\dfrac{43\pi}{2}$

$43\pi$

$86\pi$

$1{,}849\pi$

What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?

A cube has an edge length of 68 inches. A solid sphere with a radius of $34$ inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

149,796

164,500

190,955

310,800

A right rectangular prism has a length of 11 meters, a width of 8 meters, and a height of 10 meters. What is the volume, in cubic meters, of the prism?

The figure shown is a right circular cylinder with a radius of $r$ and height of $h$. A second right circular cylinder (not shown) has a volume that is $392$ times as large as the volume of the cylinder shown. Which of the following could represent the radius $R$, in terms of $r$, and the height $H$, in terms of $h$, of the second cylinder?

$R = 8r$ and $H = 7h$

$R = 8r$ and $H = 49h$

$R = 7r$ and $H = 8h$

$R = 49r$ and $H = 8h$

A right circular cylinder has a volume of $377$ cubic centimeters. The area of the base of the cylinder is $13$ square centimeters. What is the height, in centimeters, of the cylinder?

Note: Figure not drawn to scale.
The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?

A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?

164

1,681

10,086

68,921

The length of the edge of the base of a right square prism is 6 units. The volume of the prism is 2,880 cubic units. What is the height, in units, of the prism?

$4\sqrt{30}$

$36$

$24\sqrt{5}$

$80$

A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

$16\pi$

$96\pi$

$192\pi$

$768\pi$

Square A has side lengths that are 246 times the side lengths of square B. The area of square A is $k$ times the area of square B. What is the value of $k$?

60,516

492

246

123

A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?

16,000 pi

20,000 pi

25,000 pi

31,250 pi

Right rectangular prism X is similar to right rectangular prism Y. The surface area of right rectangular prism X is 58 square centimeters ($\text{cm}^2$), and the surface area of right rectangular prism Y is 1,450 $\text{cm}^2$. The volume of right rectangular prism Y is 1,250 cubic centimeters ($\text{cm}^3$). What is the sum of the volumes, in $\text{cm}^3$, of right rectangular prism X and right rectangular prism Y?

A rectangle has an area of 63 square meters and a length of 9 meters. What is the width, in meters, of the rectangle?

567

A sphere has a radius of $\dfrac{17}{5}$ feet. What is the volume, in cubic feet, of the sphere?

$\dfrac{5\pi}{17}$

$\dfrac{68\pi}{15}$

$\dfrac{32\pi}{5}$

$\dfrac{19{,}652\pi}{375}$

A right circular cylinder has a height of 8 meters (m) and a base with a radius of 12 m. What is the volume, in $\text{m}^3$, of the cylinder?

$8\pi$

$20\pi$

$768\pi$

$1{,}152\pi$

Rectangle $ABCD$ is similar to rectangle $EFGH$. The area of rectangle $ABCD$ is 648 square inches, and the area of rectangle $EFGH$ is 72 square inches. The length of the longest side of rectangle $ABCD$ is 36 inches. What is the length, in inches, of the longest side of rectangle $EFGH$?

The floor of a ballroom has an area of $600$ square meters. An architect creates a scale model of the floor of the ballroom, where the length of each side of the model is $\frac{1}{10}$ times the length of the corresponding side of the actual floor of the ballroom. What is the area, in square meters, of the scale model?

$6$

$10$

$60$

$150$

A cube has a volume of $474{,}552$ cubic units. What is the surface area, in square units, of the cube?

The perimeter of triangle $ABC$ is 17 inches, the length of side $AB$ is 4 inches, and the length of side $AC$ is 7 inches. What is the length, in inches, of side $BC$?

A right circular cone has a height of $22$ centimeters (cm) and a base with a diameter of $6$ cm. The volume of this cone is $n\pi$ cm³. What is the value of $n$?

A rectangle has a length of $3$ units and a width of $39$ units. Which expression gives the area, in square units, of this rectangle?

$2(3 + 39)$

$2(3 \cdot 39)$

$3 + 39$

$3 \cdot 39$

The table gives the perimeters of similar triangles $TUV$ and $XYZ$, where $\overline{TU}$ corresponds to $\overline{XY}$. The length of $\overline{TU}$ is 6.
Perimeter
Triangle $TUV$
50
Triangle $XYZ$
150
What is the length of $\overline{XY}$?

A circle has a circumference of $31\pi$ centimeters. What is the diameter, in centimeters, of the circle?

Circle $K$ has a radius of $4$ millimeters (mm). Circle $L$ has an area of $100\pi$ mm$^2$. What is the total area, in mm$^2$, of circles $K$ and $L$?

$14\pi$

$28\pi$

$56\pi$

$116\pi$

A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, $V$, in cubic inches, of such containers, where $r$ is the radius, in inches?

V = 4πr^3

V = π(2r)^3

V = πr^2 + 4πr

V = πr^3 + 4πr^2

Rectangle P has an area of 72 square inches. If a rectangle with an area of 20 square inches is removed from rectangle P, what is the area, in square inches, of the resulting figure?

Parallelogram $ABCD$ is similar to parallelogram $PQRS$. The length of each side of parallelogram $PQRS$ is 2 times the length of its corresponding side of parallelogram $ABCD$. The area of parallelogram $ABCD$ is 5 square centimeters. What is the area, in square centimeters, of parallelogram $PQRS$?

Rectangles $ABCD$ and $EFGH$ are similar. The length of each side of $EFGH$ is 6 times the length of the corresponding side of $ABCD$. The area of $ABCD$ is 54 square units. What is the area, in square units, of $EFGH$?

324

1,944

Triangle $ABC$ and triangle $DEF$ are similar triangles, where $\overline{AB}$ and $\overline{DE}$ are corresponding sides. If $DE = 2AB$ and the perimeter of triangle $ABC$ is 20, what is the perimeter of triangle $DEF$?

120

A rectangular poster has an area of $360$ square inches. A copy of the poster is made in which the length and width of the original poster are each increased by $20\%$. What is the area of the copy, in square inches?

A right rectangular prism has a length of $28$ centimeters (cm), a width of $15$ cm, and a height of $16$ cm. What is the surface area, in $\text{cm}^2$, of the right rectangular prism?

What is the area, in square centimeters, of a rectangle with a length of $34$ centimeters (cm) and a width of $29$ cm?

The lengths of two sides of a triangle are 4 centimeters and 6 centimeters. If the perimeter of the triangle is 18 centimeters, what is the length, in centimeters, of the third side of this triangle?

A right circular cone has a volume of $\frac{1}{3}\pi$ cubic feet and a height of 9 feet. What is the radius, in feet, of the base of the cone?

$\frac{1}{3}$

$\frac{1}{\sqrt{3}}$

$\sqrt{3}$

SAT: Geometry & Trig - Area and Volume

SAT: Geometry & Trig - Area and Volume

The length of each edge of a box is $29$ inches. Each side of the box is in the shape of a square. The box does not have a lid. What is the exterior surface area, in square inches, of this box without a lid?

A right circular cylinder has a volume of $45\pi$. If the height of the cylinder is $5$, what is the radius of the cylinder?

Square A has side lengths that are $16$ times the side lengths of square B. The area of square A is $k$ times the area of square B. What is the value of $k$?

What is the area, in square inches, of a rectangle with a length of 7 inches and a width of 6 inches?

The side length of a square is 55 centimeters (cm). What is the area, in $\text{cm}^2$, of the square?

Triangle R has an area of 80 square centimeters ($\text{cm}^2$). Square S has side lengths of 4 cm. What is the total area of triangle R and square S, in $\text{cm}^2$?

What is the length of one side of a square that has the same area as a circle with radius $2$?

A right square prism has a height of 14 units. The volume of the prism is $2{,}016$ cubic units. What is the length, in units, of an edge of the base?

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

The circumference of the base of a right circular cylinder is $20\pi$ meters, and the height of the cylinder is 6 meters. What is the volume, in cubic meters, of the cylinder?

The area of a square is 64 square inches. What is the side length, in inches, of this square?

A circle has a radius of 43 meters. What is the area, in square meters, of the circle?

The three points shown define a circle. The circumference of this circle is $k\pi$, where $k$ is a constant. What is the value of $k$?

Question: What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?

A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

A right rectangular prism has a length of 11 meters, a width of 8 meters, and a height of 10 meters. What is the volume, in cubic meters, of the prism?

A right circular cylinder has a volume of $377$ cubic centimeters. The area of the base of the cylinder is $13$ square centimeters. What is the height, in centimeters, of the cylinder?

The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?

A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?

The length of the edge of the base of a right square prism is 6 units. The volume of the prism is 2,880 cubic units. What is the height, in units, of the prism?

A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

The length of each edge of a box is $29$ inches. Each side of the box is in the shape of a square. The box does not have a lid. What is the exterior surface area, in square inches, of this box without a lid?

A right circular cylinder has a volume of $45\pi$. If the height of the cylinder is 5, what is the radius of the cylinder?

Square A has side lengths that are $16$ times the side lengths of square B. The area of square A is $k$ times the area of square B. What is the value of $k$?

What is the area, in square inches, of a rectangle with a length of 7 inches and a width of 6 inches?

The side length of a square is 55 centimeters (cm). What is the area, in $\text{cm}^2$, of the square?

Triangle R has an area of 80 square centimeters ($\text{cm}^2$). Square S has side lengths of 4 cm. What is the total area of triangle R and square S, in $\text{cm}^2$?

What is the length of one side of a square that has the same area as a circle with radius $2$?

A right square prism has a height of 14 units. The volume of the prism is $2{,}016$ cubic units. What is the length, in units, of an edge of the base?

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

The circumference of the base of a right circular cylinder is $20\pi$ meters, and the height of the cylinder is 6 meters. What is the volume, in cubic meters, of the cylinder?

The area of a square is 64 square inches. What is the side length, in inches, of this square?

A circle has a radius of 43 meters. What is the area, in square meters, of the circle?

What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?

A cube has an edge length of 68 inches. A solid sphere with a radius of $34$ inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

A right rectangular prism has a length of 11 meters, a width of 8 meters, and a height of 10 meters. What is the volume, in cubic meters, of the prism?

A right circular cylinder has a volume of $377$ cubic centimeters. The area of the base of the cylinder is $13$ square centimeters. What is the height, in centimeters, of the cylinder?

Note: Figure not drawn to scale.The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?

A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?

The length of the edge of the base of a right square prism is 6 units. The volume of the prism is 2,880 cubic units. What is the height, in units, of the prism?

A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

Square A has side lengths that are 246 times the side lengths of square B. The area of square A is $k$ times the area of square B. What is the value of $k$?

A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?

A rectangle has an area of 63 square meters and a length of 9 meters. What is the width, in meters, of the rectangle?

A sphere has a radius of $\dfrac{17}{5}$ feet. What is the volume, in cubic feet, of the sphere?

A right circular cylinder has a height of 8 meters (m) and a base with a radius of 12 m. What is the volume, in $\text{m}^3$, of the cylinder?

Rectangle $ABCD$ is similar to rectangle $EFGH$. The area of rectangle $ABCD$ is 648 square inches, and the area of rectangle $EFGH$ is 72 square inches. The length of the longest side of rectangle $ABCD$ is 36 inches. What is the length, in inches, of the longest side of rectangle $EFGH$?

A cube has a volume of $474{,}552$ cubic units. What is the surface area, in square units, of the cube?

The perimeter of triangle $ABC$ is 17 inches, the length of side $AB$ is 4 inches, and the length of side $AC$ is 7 inches. What is the length, in inches, of side $BC$?

A right circular cone has a height of $22$ centimeters (cm) and a base with a diameter of $6$ cm. The volume of this cone is $n\pi$ cm3. What is the value of $n$?

A rectangle has a length of $3$ units and a width of $39$ units. Which expression gives the area, in square units, of this rectangle?

The table gives the perimeters of similar triangles $TUV$ and $XYZ$, where $\overline{TU}$ corresponds to $\overline{XY}$. The length of $\overline{TU}$ is 6.PerimeterTriangle $TUV$50Triangle $XYZ$150What is the length of $\overline{XY}$?

A circle has a circumference of $31\pi$ centimeters. What is the diameter, in centimeters, of the circle?

Circle $K$ has a radius of $4$ millimeters (mm). Circle $L$ has an area of $100\pi$ mm$^2$. What is the total area, in mm$^2$, of circles $K$ and $L$?

Rectangle P has an area of 72 square inches. If a rectangle with an area of 20 square inches is removed from rectangle P, what is the area, in square inches, of the resulting figure?

Rectangles $ABCD$ and $EFGH$ are similar. The length of each side of $EFGH$ is 6 times the length of the corresponding side of $ABCD$. The area of $ABCD$ is 54 square units. What is the area, in square units, of $EFGH$?

Triangle $ABC$ and triangle $DEF$ are similar triangles, where $\overline{AB}$ and $\overline{DE}$ are corresponding sides. If $DE = 2AB$ and the perimeter of triangle $ABC$ is 20, what is the perimeter of triangle $DEF$?

A rectangular poster has an area of $360$ square inches. A copy of the poster is made in which the length and width of the original poster are each increased by $20\%$. What is the area of the copy, in square inches?

A right rectangular prism has a length of $28$ centimeters (cm), a width of $15$ cm, and a height of $16$ cm. What is the surface area, in $\text{cm}^2$, of the right rectangular prism?

What is the area, in square centimeters, of a rectangle with a length of $34$ centimeters (cm) and a width of $29$ cm?

The lengths of two sides of a triangle are 4 centimeters and 6 centimeters. If the perimeter of the triangle is 18 centimeters, what is the length, in centimeters, of the third side of this triangle?

A right circular cone has a volume of $\frac{1}{3}\pi$ cubic feet and a height of 9 feet. What is the radius, in feet, of the base of the cone?

The length of each edge of a box is $29$ inches. Each side of the box is in the shape of a square. The box does not have a lid. What is the exterior surface area, in square inches, of this box without a lid?

A right circular cylinder has a volume of $45\pi$. If the height of the cylinder is $5$, what is the radius of the cylinder?

Square A has side lengths that are $16$ times the side lengths of square B. The area of square A is $k$ times the area of square B. What is the value of $k$?

What is the area, in square inches, of a rectangle with a length of 7 inches and a width of 6 inches?

The side length of a square is 55 centimeters (cm). What is the area, in $\text{cm}^2$, of the square?

Triangle R has an area of 80 square centimeters ($\text{cm}^2$). Square S has side lengths of 4 cm. What is the total area of triangle R and square S, in $\text{cm}^2$?

What is the length of one side of a square that has the same area as a circle with radius $2$?

A right square prism has a height of 14 units. The volume of the prism is $2{,}016$ cubic units. What is the length, in units, of an edge of the base?

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

The circumference of the base of a right circular cylinder is $20\pi$ meters, and the height of the cylinder is 6 meters. What is the volume, in cubic meters, of the cylinder?

The area of a square is 64 square inches. What is the side length, in inches, of this square?

A circle has a radius of 43 meters. What is the area, in square meters, of the circle?

The three points shown define a circle. The circumference of this circle is $k\pi$, where $k$ is a constant. What is the value of $k$?

Question: What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?

A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

A right rectangular prism has a length of 11 meters, a width of 8 meters, and a height of 10 meters. What is the volume, in cubic meters, of the prism?

Note: Figure not drawn to scale.
The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?

A right circular cone has a height of $22$ centimeters (cm) and a base with a diameter of $6$ cm. The volume of this cone is $n\pi$ cm³. What is the value of $n$?

The table gives the perimeters of similar triangles $TUV$ and $XYZ$, where $\overline{TU}$ corresponds to $\overline{XY}$. The length of $\overline{TU}$ is 6.
Perimeter
Triangle $TUV$
50
Triangle $XYZ$
150
What is the length of $\overline{XY}$?

Note: Figure not drawn to scale.
The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?

A right circular cone has a height of $22$ centimeters (cm) and a base with a diameter of $6$ cm. The volume of this cone is $n\pi$ cm³. What is the value of $n$?

The table gives the perimeters of similar triangles $TUV$ and $XYZ$, where $\overline{TU}$ corresponds to $\overline{XY}$. The length of $\overline{TU}$ is 6.
Perimeter
Triangle $TUV$
50
Triangle $XYZ$
150
What is the length of $\overline{XY}$?