Calculate the volume of a pyramid and cone
Objectives
Student will be able to:
use a formula to find the volume of a pyramid.
use a formula to find the volume of a cone.
Introduction
To calculate the volume of a pyramid, start with the formula for the volume of a rectangular prism.
The area of the base of the prism, which is the product of the length and width of the base, is represented by
B
. The height of the prism is represented by
h
.
A pyramid has
the volume of a rectangular prism with the same base measurements. So the formula for the volume of a pyramid is:
Calculate the volume of this pyramid.
The formula for the volume of a cylinder is also
However, to find the area of the base, or
B
, multiply
A cone has
the volume of a cylinder with the same base measurements. The formula for the volume of a cone is:
Remember, to find the area of the base multiply
Examples
1.
Find the volume of the cone. Use
and round to the nearest hundredth.
Remember to use the formula for the area of a circle,
, to find the base, since the base of a cone is a circle.
The volume of the cone is approximately 669.87 cubic inches.
2.
Find the volume of the pyramid.
The volume of the pyramid is 12 cubic feet.
Try Together
Complete the exercises. Show all work.
1.
Calculate the volume of the pyramid.
Check student's work.
2.
Find the volume of the cone. Round to the nearest hundredth. Use
Check student's work.
Please evaluate the student's answers:
Excellent
Good
Okay