Lesson 4: Cylinders and Cones

Property

Volume is the amount of space contained within a three-dimensional object. It is measured in cubic units, such as cubic feet or cubic centimeters.

Cylinder Volume Formula:

Property

To find the height ($h$) of a cylinder given its volume ($V$) and radius ($r$), you can rearrange the volume formula $V = \pi r^2 h$. By dividing both sides by the area of the base, $\pi r^2$, we get the formula for height:

Examples

Property

The volume $V$ of a cone with radius $r$ and height $h$ is given by the formula:

Examples

• A cone with a radius of $3$ cm and a height of $5$ cm has a volume of $V = \frac{1}{3}\pi (3^2)(5) = 15\pi$ cm$^3$.
• A cone with a radius of $4$ inches and a height of $9$ inches has a volume of $V = \frac{1}{3}\pi (4^2)(9) = 48\pi$ inches$^3$.

Explanation

The volume of a cone measures the amount of space it occupies. This formula shows that the volume depends on the radius of its circular base ($r$) and its perpendicular height ($h$). An important relationship to note is that a cone''s volume is exactly one-third the volume of a cylinder with the same radius and height. To calculate the volume, substitute the known values for the radius and height into the formula.