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

How to find the volume of cones and pyramids, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

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 Btimes 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 Btimes 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:

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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 Btimes h)

(B=10times 5=50)

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

(=frac{1}{3}times Btimes h=frac{1}{3}times 50times 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 Btimes h)

(B=6times 11=66)

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

(=frac{1}{3}times Btimes h=frac{1}{3}times 66times 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})

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