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
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