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
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
Vocabulary Review: Complete each definition and then provide an example of each vocabulary word.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
The combination of two or more geometric shapes | arrow_right_alt | circumference |
The 2D shape that is exposed when a slice is made through a 3D object. | arrow_right_alt | composite figure |
The distance around a circle is the | arrow_right_alt | area |
A circle’s _________________________ is the distance from the edge of the circle to its center. | arrow_right_alt | cross section |
Volume is measured in | arrow_right_alt | radius |
The number of square units that cover a shape is the _________________________ of the a shape. | arrow_right_alt | cubic units (example: cm3) |
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.
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.
The circumference of a bicycle tire is 126.5 centimeters. What is the diameter of the tire? Use 3.14 for π.
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
The diameter of a pizza is 12 inches. What is the area?
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
The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
A circular plate has circumference 24 inches. What is the area of this plate? Use 3.14 for π.
Steps:
Use the equation for circumference to solve for radius.
Use your value for radius to solve for the area.
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.
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?
formulas: SA of a rectangle = length • width. SA of a triangle =
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.
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.
Kara wants to paint the four outside walls of her dog’s house. She will not paint the roof or the door on the front of the house. What is the area of the surface that Kara needs to paint?
Steps:
Divide the four sides of the house up into our basic shapes (rectangles, squares, triangles, and circles).
Draw a sketch of each shape with its dimensions.
Determine the surface area of each shape.
Multiply the surface area of each shape by the number of times it occurs.
Add the surface area of all shapes, but subtract the surface area of the front door.
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, the green shape has a surface area of ________ ft2.
Steps:
Divide the shape up into our basic shapes (rectangles, squares, triangles, and circles). HINT: The blue area is two half circles with the same diameter, which equals one full circle.
Draw a sketch of each shape with its dimensions.
Determine the surface area of each shape.
Subtract the surface area of the smaller shape from the larger shape.
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.
Holly has a gift box that is shaped like a regular hexagonal prism.
The volume of the box is ___________ in3.
Steps:
Use the formula B = 3ba to find the surface area of the Base.
Use the formula V = Bh to find the volume of the hexagonal prism.
A building that is used for storage has the dimensions shown.
The volume of the building is _____________ ft3.
Steps:
Find the volume of each shape: triangular prism and rectangular prism.
Add the volume of each shape together.