8.7 Surface Area Day 2

8.7 Surface Area – Day 2

Investigation 2: Surface Area of Pyramids

1.) If you wanted to find the surface area of the square pyramid below, what measurements would you need in order to find the surface area?

2.) Make up numbers for those measurements and find the surface area of the pyramid. Show all work.

3.) Suppose you had a pyramid whose base was a regular n-gon (making all of the lateral faces identical triangles.) See illustration below.

a.) Write a formula for each of the triangular lateral faces. (Use the variables from the picture above.)

b.) Write a formula for all of the triangular faces combined.

c.) Write a formula for the base (remember, it looks like an octagon, but we are going to use n for the number of sides.) Note: we wrote this formula when we did section 8.4, you just have to remember it.

d.) Using your answers from part b and c, write a formula for the surface area of any pyramid with a regular polygon base. 4.) The great pyramid in Egypt has a square base with side length of about 756 feet, a height of about 481 feet and a slant height of about 612 feet. Use your formula to calculate the surface area.

Investigation 2: Surface Area of a Cone

1.) Write an expression for the area of the base of the cone.

2.) Looking at the illustration, write an expression for the area of the lateral surface of the cone.

3.) Write a formula for the surface area of the cone.

4.) The ice cream cone below has a slant height of 3 inches and a diameter of 1 7/8 inches. Use your formula to find the amount of “cone” needed to make the cone.