Volume of a Cone Math Example 3

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

Example 3

easy
A cone and a cylinder have the same radius and height. The cylinder's volume is 90π90\pi cm³. What is the cone's volume?

Solution

  1. 1
    Step 1: The cone's volume is 13\frac{1}{3} the cylinder's volume (for the same radius and height).
  2. 2
    Step 2: Cone volume =13×90π=30π= \frac{1}{3} \times 90\pi = 30\pi cm³.

Answer

30π30\pi cm³.
A fundamental relationship: a cone has exactly 13\frac{1}{3} the volume of a cylinder with the same base radius and height. This is because the formula Vcone=13πr2hV_{\text{cone}} = \frac{1}{3}\pi r^2 h is exactly one-third of Vcylinder=πr2hV_{\text{cylinder}} = \pi r^2 h.

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.

Learn more about Volume of a Cone →

More Volume of a Cone Examples

Example 1 easy

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

Example 2 medium

An ice cream cone has a volume of [formula] cm³ and a radius of 5 cm. Find the height of the cone.

Example 4 hard

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

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