Surface Area and Volume of Prisms part 1

Surface Area and Volume of Prisms part 1

Lateral Surfaces the surfaces that make up the - parts of the shape between the bases.

Cylinder = base shape: circle. lateral shape: rectangle. Prism = base shape: depends on name. lateral shape: rectangles. Pyramid = base shape: depends on name. lateral shape: triangles.

Lateral Area of a Prism The lateral area of a prism is the sum of the areas of the lateral faces. Lateral Face—a lateral face of a prism is a face that joins the bases of the prism The lateral area of the prism is the total area of its lateral faces.

1 Find the surface area of each rectangular prism.

2 Find the surface area of each rectangular prism.

3 Ms. Adventure went on a trip around the world. In the Netherlands, she tasted Dutch cheese. The piece of cheese has the shape of a triangular prism. How much surface area is there for mold to grow on?

4 What is the surface area of the triangular prism?

Part 3 Example 1 When a base of a prism is a regular polygon, you can decompose the polygon to find its area. You can decompose a regular hexagon into 6 equilateral triangles. The 6 triangles are the same size. After you find the area of 1 triangle, you can multiply the area by 6 to find the area of the entire hexagon.

5 Ms. Adventure wants to make a box like one she saw in Japan. She plans to cover the box with paper. The box has the shape of a regular hexagonal prism. To the nearest square inch, how much paper does Ms. Adventure need to cover the box?

6 To the nearest square inch, what is the surface area of the regular hexagonal prism?

Homework: Surface Area of Prisms Worksheet

Volume of a Prism The formula for the volume of a prism equals the area of the base times the height. Or, V = Bh Area of the base x height = (length x width) x height

Find the Volume of the Prism. V = area of base · height V = Bh V = (9) (2) (3) V = 54 ft³

Find the Volume of the Prism. V = side length cubed V = s³ V = (3) (3) V = 27 ft³

Find the Volume of the Prism. 7

Find the Volume of each Prism. What is the volume of a cube with edge length ¾ ft. ? V = side length cubed V = s³ V = ( 3/4 ) V = 27/64 ft³

Find the Volume the Prism. 8

Find the Volume of each Prism. 9

Find the Volume of the Prism Ms. Adventure’s Japanese box has the shape of a regular hexagonal prism. To the nearest cubic inch, what is the amount of space inside the box? 10

Find the Volume of the Prism 11

HW: Volume of Prisms Worksheet