Chapter 8 Review: Part 2**

In Chapter 8 we learned about multiple aspects of Geometry. Our Part 2 Review will cover:
Area and Circumference of Circles
Cross Sections of Rectangular Prisms and Regular Pyramids
Surface Area and Volume

2

Vocabulary Review: Complete each definition and then provide an example of each vocabulary word.

Draggable item		Corresponding Item

Lesson 8-5 Solve Problems Involving Circumference of a Circle
Quick Review: The distance around a circle is called its circumference.  The number π (pi) is the ratio of the circumference of any circle to its diameter.  So when you know the diameter, d, of a circle, or its radius, r, you can determine its circumference, C, with the formula C = πd or C = 2πr.

1

The length of the minute hand of a clock is 14 inches. What is the length of the path traced by the outer tip of the minute hand in one hour? Use 3.14 for π.
formulas: 2r = d C = 2πr C = πd

1

The circumference of a bicycle tire is 126.5 centimeters. What is the diameter of the tire? Use 3.14 for π.
formulas: 2r = d C = 2πr C = πd

Lesson 8-6 Solve Problems Involving Area of a Circle
Quick Review: The area, A, of a circle can be found using the formula A = πr2, where r is the radius.  You can use 3.14 or 22/7 for π.

2

The diameter of a pizza is 12 inches. What is the area?

Steps:
Use the formula 2r = d to find the radius, r.
Use the formula A = πr2 to find the area, A.

Using the Google Calculator to find a square root
Press square root button
Enter the number you want to find the square root of
Press equal

1

The area of a circle is 153.86 square meters. What is the radius of the circle? Use 3.14 for π.

Steps:
Substitute 153.86 for A into the equation A = πr2.
Divide both sides by π.
Take the square root of both sides.

4

A circular plate has circumference 24 inches. What is the area of this plate? Use 3.14 for π.

Steps:
Use the formula C = 2πr. Substitute in 24 for C and 3.14 for π.
Solve for r.
Use the formula A = πr2. Substitute in your value of r from Step 2.
Solve for A.

Lesson 8-7 Describe Cross Sections
Quick Review: A cross-section is the two-dimensional shape exposed when a three-dimensional figure is sliced. Recognizing the shape of a cross-section can help in solving some problems.

1

The figure shows a vertical cross-section of a right rectangular pyramid. What shape is the cross-section?

2

What is the area of the vertical cross-section?
formula: SA = 1/2base • height

1

Zach wants to slice the pyramid along a horizontal plane that intersects the pyramid above its base. Describe the cross section that would be formed.

Lesson 8-8 Solve Problems Involving Composite Figures
Quick Review: A composite figure is the combination of two or more geometric shapes.  The surface area of a two- and three-dimensional composite figure will be the sum of the area of all the shapes, or faces.

4

Kara wants to paint the four outside walls of her dog’s house. She will not paint the roof. What is the area of the surface that Kara needs to paint?

3

Sarah is designing a logo. First, she paints a green square with side lengths of 5 feet. Then she uses blue paint to inscribe two semicircles as shown. What is the area of the part of the logo that is still green? Use 3.14 for π. Enter your answer in the box.

Lesson 8-9 Solve Problems Involving Volume
Quick Review: You can find the volume, V, of a prism using the formula V = Bh. In this formula, B represents the area of the base of the prism and h represents the height of the prism.  Volume is measured in cubic units.

3

Holly has a gift box that is shaped like a regular hexagonal prism. What is the volume of the box?

5

A building that is used for storage has the dimensions shown. What is the volume of the building?

Steps:
Find the volume of the triangular prism.
Find the volume of the rectangular prism.
Add the volume of both shapes together.

Draggable item		Corresponding Item
The number of square units that cover a shape is the _________________________ of the a shape.		circumference
A circle’s _________________________ is the distance from the edge of the circle to its center.		composite figure
The distance around a circle is the		area
The combination of two or more geometric shapes		cross section
Volume is measured in		radius
The 2D shape that is exposed when a slice is made through a 3D object.		cubic units (example: cm3)

Chapter 8 Review: Part 2**

Vocabulary Review: Complete each definition and then provide an example of each vocabulary word.

Lesson 8-5 Solve Problems Involving Circumference of a Circle

The length of the minute hand of a clock is 14 inches. What is the length of the path traced by the outer tip of the minute hand in one hour? Use 3.14 for π. formulas: 2r = d C = 2πr C = πd

The circumference of a bicycle tire is 126.5 centimeters. What is the diameter of the tire? Use 3.14 for π. formulas: 2r = d C = 2πr C = πd

Lesson 8-6 Solve Problems Involving Area of a Circle

The diameter of a pizza is 12 inches. What is the area?Steps: Use the formula 2r = d to find the radius, r.Use the formula A = πr2 to find the area, A.

The area of a circle is 153.86 square meters. What is the radius of the circle? Use 3.14 for π.Steps: Substitute 153.86 for A into the equation A = πr2.Divide both sides by π.Take the square root of both sides.

A circular plate has circumference 24 inches. What is the area of this​ plate? Use 3.14 for π.Steps: Use the formula C = 2πr. Substitute in 24 for C and 3.14 for π.Solve for r. Use the formula A = πr2. Substitute in your value of r from Step 2.Solve for A.

Lesson 8-7 Describe Cross Sections

The figure shows a vertical cross-section of a right rectangular pyramid. What shape is the cross-section?

What is the area of the vertical cross-section? formula: SA = 1/2base • height

Zach wants to slice the pyramid along a horizontal plane that intersects the pyramid above its base. Describe the cross section that would be formed.

Lesson 8-8 Solve Problems Involving Composite Figures

Kara wants to paint the four outside walls of her dog’s house. She will not paint the roof. What is the area of the surface that Kara needs to paint?

Sarah is designing a logo. First, she paints a green square with side lengths of 5 feet. Then she uses blue paint to inscribe two semicircles as shown. What is the area of the part of the logo that is still green? Use 3.14 for π. Enter your answer in the box.

Lesson 8-9 Solve Problems Involving Volume

Holly has a gift box that is shaped like a regular hexagonal prism. What is the volume of the box?

A building that is used for storage has the dimensions shown. What is the volume of the building?Steps: Find the volume of the triangular prism. Find the volume of the rectangular prism.Add the volume of both shapes together.

Vocabulary Review: Complete each definition and then provide an example of each vocabulary word.

Lesson 8-5 Solve Problems Involving Circumference of a Circle

The length of the minute hand of a clock is 14 inches. What is the length of the path traced by the outer tip of the minute hand in one hour? Use 3.14 for π. formulas: 2r = d C = 2πr C = πd

The circumference of a bicycle tire is 126.5 centimeters. What is the diameter of the tire? Use 3.14 for π. formulas: 2r = d C = 2πr C = πd

Lesson 8-6 Solve Problems Involving Area of a Circle

The diameter of a pizza is 12 inches. What is the area?Steps: Use the formula 2r = d to find the radius, r.Use the formula A = πr2 to find the area, A.

The area of a circle is 153.86 square meters. What is the radius of the circle? Use 3.14 for π.Steps: Substitute 153.86 for A into the equation A = πr2.Divide both sides by π.Take the square root of both sides.

A circular plate has circumference 24 inches. What is the area of this​ plate? Use 3.14 for π.Steps: Use the formula C = 2πr. Substitute in 24 for C and 3.14 for π.Solve for r. Use the formula A = πr2. Substitute in your value of r from Step 2.Solve for A.

Lesson 8-7 Describe Cross Sections

The figure shows a vertical cross-section of a right rectangular pyramid. What shape is the cross-section?

What is the area of the vertical cross-section? formula: SA = 1/2base • height

Zach wants to slice the pyramid along a horizontal plane that intersects the pyramid above its base. Describe the cross section that would be formed.

Lesson 8-8 Solve Problems Involving Composite Figures

Kara wants to paint the four outside walls of her dog’s house. She will not paint the roof. What is the area of the surface that Kara needs to paint?

Sarah is designing a logo. First, she paints a green square with side lengths of 5 feet. Then she uses blue paint to inscribe two semicircles as shown. What is the area of the part of the logo that is still green? Use 3.14 for π. Enter your answer in the box.

Lesson 8-9 Solve Problems Involving Volume

Holly has a gift box that is shaped like a regular hexagonal prism. What is the volume of the box?

A building that is used for storage has the dimensions shown. What is the volume of the building?Steps: Find the volume of the triangular prism. Find the volume of the rectangular prism.Add the volume of both shapes together.

The length of the minute hand of a clock is 14 inches. What is the length of the path traced by the outer tip of the minute hand in one hour? Use 3.14 for π.
formulas: 2r = d C = 2πr C = πd

The circumference of a bicycle tire is 126.5 centimeters. What is the diameter of the tire? Use 3.14 for π.
formulas: 2r = d C = 2πr C = πd

The diameter of a pizza is 12 inches. What is the area?

Steps:
Use the formula 2r = d to find the radius, r.
Use the formula A = πr2 to find the area, A.

The area of a circle is 153.86 square meters. What is the radius of the circle? Use 3.14 for π.

Steps:
Substitute 153.86 for A into the equation A = πr2.
Divide both sides by π.
Take the square root of both sides.

A circular plate has circumference 24 inches. What is the area of this plate? Use 3.14 for π.

Steps:
Use the formula C = 2πr. Substitute in 24 for C and 3.14 for π.
Solve for r.
Use the formula A = πr2. Substitute in your value of r from Step 2.
Solve for A.

What is the area of the vertical cross-section?
formula: SA = 1/2base • height

A building that is used for storage has the dimensions shown. What is the volume of the building?

Steps:
Find the volume of the triangular prism.
Find the volume of the rectangular prism.
Add the volume of both shapes together.

The length of the minute hand of a clock is 14 inches. What is the length of the path traced by the outer tip of the minute hand in one hour? Use 3.14 for π.
formulas: 2r = d C = 2πr C = πd

The circumference of a bicycle tire is 126.5 centimeters. What is the diameter of the tire? Use 3.14 for π.
formulas: 2r = d C = 2πr C = πd

The diameter of a pizza is 12 inches. What is the area?

Steps:
Use the formula 2r = d to find the radius, r.
Use the formula A = πr2 to find the area, A.

The area of a circle is 153.86 square meters. What is the radius of the circle? Use 3.14 for π.

Steps:
Substitute 153.86 for A into the equation A = πr2.
Divide both sides by π.
Take the square root of both sides.

A circular plate has circumference 24 inches. What is the area of this plate? Use 3.14 for π.

Steps:
Use the formula C = 2πr. Substitute in 24 for C and 3.14 for π.
Solve for r.
Use the formula A = πr2. Substitute in your value of r from Step 2.
Solve for A.

What is the area of the vertical cross-section?
formula: SA = 1/2base • height

A building that is used for storage has the dimensions shown. What is the volume of the building?

Steps:
Find the volume of the triangular prism.
Find the volume of the rectangular prism.
Add the volume of both shapes together.