1. Solving Surface Area Problems

2. Warm Up

3. Number of Lateral Faces
Complete the table.
Prism
Number of Lateral Faces
Number of Bases
Rectangular Prism
Cube
Triangular Prism

4. The formula S = Ph + 2B is a general formula for finding the surface area of a prism.
The P in the surface area formula represents the perimeter of the base of the prism.
The value of h in the surface area formula is the height of the prism.
The formula used for finding B depends on the shape of the base of the prism.
To find the surface area of a composite figure, find the surface area of each of the prisms that comprise the composite figure, then subtract twice those parts not on the surface.

5. A small cube with edges measuring 5 cm sits on top of a larger cube with edges measuring 10 cm. How does the surface area of the two separate figures differ from the surface area of the composite figure?

6. How can you find the surface area of a figure made up of cubes and prisms? Find the surface area of each of the cubes and prisms that make up the solid. Add the surface areas, and subtract the areas of any parts that are not on the surface.

7. How do you decide which dimension is the length, width and height of the prism? First determine which side is a base. The longer edge on a base is commonly called the length, the shorter edge is commonly called the width, and the other edge is commonly called the height.

8. Henry stores the arrowheads he has found in a box the shape of a rectangular prism. The box is 14 inches long, 12 inches wide and 2 inches high. He plans to paint the exterior of the box. How many square inches does he have to paint?

9. How does knowing how to find the surface area of prisms help you when finding the surface area of a composite solid? When a composite solid is made up of more than one prism, adding the surface area of each of the prisms and then subtracting any area not on the surface allows you to find the total surface area.

10. What is the surface area of the milk carton?

11. Marco and Elaine are building a stand like the one shown to display trophies. What is the surface area of the stand?
Marco and Elaine want to paint the entire stand silver. A can of paint covers 25 square feet and costs $6.79. They set aside $15 for paint. Is that enough? Explain.

12. Henry wants to cover the box shown with paper without any overlap
Henry wants to cover the box shown with paper without any overlap. How many square centimeters will be covered with paper? Suppose the length and width of the box doubled. Does the surface area double? Explain.

13. Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengths of 2.5 feet and a height of 3.5 feet. Compare the amount of paint she would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism.

14. The oatmeal box shown is shaped like a cylinder
The oatmeal box shown is shaped like a cylinder. Use a net to find the surface area S of the oatmeal box to the nearest tenth. Then find the number of square feet of cardboard needed for 1,500 oatmeal boxes. Round your answer to the nearest whole number.

15. Exit Ticket Find the surface area of each solid figure.