Volume of a Cone Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

A cone has a radius of 6 cm and a height of 9 cm. Find its volume. Leave your answer in terms of

\pi

1
Step 1: Write the formula: $V = \frac{1}{3}\pi r^2 h$ .
2
Step 2: Substitute: $V = \frac{1}{3}\pi (6)^2(9) = \frac{1}{3}\pi \times 36 \times 9 = \frac{1}{3} \times 324\pi$ .
3
Step 3: Simplify: $V = 108\pi$ cm³.

Answer

V = 108\pi

cm³.

The cone formula

V = \frac{1}{3}\pi r^2 h

is exactly one-third the volume of a cylinder with the same base and height. This factor of

\frac{1}{3}

can be demonstrated by filling a cone with water and pouring it into a cylinder three times to fill it completely.

About Volume of a Cone

The amount of three-dimensional space inside a cone, which is exactly one-third the volume of a cylinder with the same base and height.

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A cone has a slant height of 13 cm and a radius of 5 cm. Find its volume. (Hint: use the Pythagorean