Surface Area and Volume: Surface Area and Volume of Pyramids and Cones

Warm-Up Icon Section Warm-Up

The following section, like the previous section, will require you to be able to find area and side lengths of a variety of three-dimensional figures.  To do this, you need to be able to visualize the figure and work with the information you are given.  Let’s practice a bit before we start this section.

think icon Think & Click: Section Warm-Up

Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

1. What is the height of this triangle?

Triangle with side lengths 10, 10 and 4
Triangle

 

Because this is an isosceles triangle, the height can be drawn and a right triangle is made.  The base is bisected.

Triangle with side lengths 10, 10 and 4, with right triangle drawn
Triangle

 

22 + h2 = 102
4 + h2 = 100
h2 = 96
h ≈ 9.798

2.  Find the height of this figure.

Square Pyramid with base 6 by 6 and slant height 5
Square Pyramid

 

Notice that the height makes a right triangle with half of the base and the slant height.

Square Pyramid with base 6 by 6 and slant height 5, right triangle with legs 3 and h and hypotenuse 5
Square Pyramid

 

32 + h2 = 52
9 + h2 = 25
h2 = 16
h = 4