How to Find the Volume of Cones and Pyramids? (+FREE Worksheet!)

Volume of Cones: \(\frac{1}{3}\)\(\times\)area of base\(\times\)height

This relation, based on mathematical symbols, will be as follows:

\(V=\frac{1}{3}\times B\times h=\frac{1}{3}πr^2h\)

Note that in the above relation, \(V\) is the symbol of volume, \(r\) and \(h\) represent the radius of the cone and its height.

A pyramid is a three-dimensional geometric figure that has a polygon base and triangular faces pointed towards the top point, called the vertex. The height of a pyramid is a line that is from the top of the pyramid to its base and is perpendicular to the surface of the base.

To calculate the volume of a pyramid, we must first find the area of the base surface and then multiply it by its height. Divide the resulting value by 3, and finally, the volume of the pyramid is obtained. Therefore, the formula for calculating the volume of the pyramid will be as follows:

Volume of a pyramid: \(\frac{1}{3}\)\(\times\)area of base\(\times\)height

The above formula is based on mathematical symbols as follows:

\(V=\frac{1}{3}\times B\times h\)

Note that the above formula \(V\) symbolizes the volume of the pyramid, \(b\) is the area of the base surface, and \(h\) is the height of the pyramid.

Finding Volume of Cones and Pyramids – Example 1:

Find the volume of the following cone. \((π=3.14)\)

Solution:

Use the formula for the volume of cones\(=\frac{1}{3}πr^2h\)

Substitute \(6\) for \(r\) and \(15\) for \(h\):

\(=\frac{1}{3}πr^2h=\)\(\frac{1}{3} \times 3.14 \times (6)^2 \times (15)=565.2 {cm}^3\)

Finding Volume of Cones and Pyramids – Example 2:

Find the volume of the pyramid.

Solution:

The volume of a pyramid\(=\frac{1}{3}\times B\times h\)

\(B=10\times 5=50\)

Substitute \(50\) for \(B\) and \(12\) for \(h\):

\(=\frac{1}{3}\times B\times h=\frac{1}{3}\times 50\times 12=200 {in}^3\)

Finding Volume of Cones and Pyramids – Example 3:

Find the volume of the following cone. \((π=3.14)\)

Solution:

Use the formula for the volume of cones\(=\frac{1}{3}πr^2h\)

Substitute \(5\) for \(r\) and \(20\) for \(h\):

\(=\frac{1}{3}πr^2h=\)\(\frac{1}{3} \times 3.14 \times (5)^2 \times (20)=523.33 {cm}^3\)

Finding Volume of Cones and Pyramids – Example 4:

Find the volume of the pyramid.

Solution:

The volume of a pyramid\(=\frac{1}{3}\times B\times h\)

\(B=6\times 11=66\)

Substitute \(66\) for \(B\) and \(11\) for \(h\):

\(=\frac{1}{3}\times B\times h=\frac{1}{3}\times 66\times 11=242 {cm}^3\)

Exercises for Finding Volume of Cones and Pyramids

Find the volume of each figure.\((π=3.14)\)

2.

3.

4.

1. \(\color{blue}{V≈1,272 {cm}^3}\)
2. \(\color{blue}{V=286 {in}^3}\)
3. \(\color{blue}{V≈3,014 {cm}^3}\)
4. \(\color{blue}{V=585 {cm}^3}\)