Section 12.5 Volumes of Pyramids and Cones

Goal 1: __ I can find the volume of a pyramid___________________________________

Goal 2: __I can find the volume of a cone______________________________________

Pre-learning

1. Find the volume of a cube with a side of 5. If a pyramid was fit inside the cube, what is its

volume?

Learning

The Great Pyramid of Giza was built around 2450 BC, and it took more than 30 years to build.

More than two million large stones ranging in weight from 1,000 to 2,000 kilograms each were

used. The base of the pyramid is a square and if you were to walk completely around the base

it would be a distance of 900 meters (more than 1/2 a mile). The height of the pyramid is 148

meters (about the height of a 50 story building).

What is the volume of the pyramid in cubic meters?

Formulas Prism Pyramid Cylinder Cone Sphere

Lateral Area

Surface

Area

Volume

5 5

1.) A pyramid has a base that is a regular

hexagon. Each side has length 8”. The pyramid is

12” tall. What is the approximate volume of the

pyramid?

2.) A pyramid has a square base with a diagonal

of 18. Each lateral edge measures 15. Find the

volume of the pyramid.

3.

a) Find the volume of the upper cone (the solid

above the cross section).

b) Find x and the volume of the frustum (the solid

below the cross section).

4. A cube has a surface area of 54 square

centimeters.

a) Find the volume of the cube.

b) Find the diagonal of the cube.

x

8

4

6