Skill: Calculate the volume of cylinders

The volume of a cylinder is the space inside it. Find it using

$$V=\pi r^2h$$

where:

• $r$ is the radius of the circular base
• $h$ is the perpendicular height
• $\pi$ can be left exact or approximated as $3.14$

Remember: if you are given the diameter, divide it by $2$ to find the radius.

Example: A cylinder has a diameter of $10\text{ cm}$ and a height of $7\text{ cm}$. Find its volume.

Step 1: Find the radius.

The radius is half the diameter:

$$r=\frac{10}{2}=5\text{ cm}$$

Step 2: Substitute the values into the formula.

$$V=\pi(5)^2(7)$$

Step 3: Calculate.

$$V=\pi(25)(7)=175\pi\text{ cm}^3$$

This is the exact volume. Using $\pi\approx3.14$:

$$V\approx175(3.14)=549.5\text{ cm}^3$$

So, the cylinder’s volume is

$$\boxed{175\pi\text{ cm}^3\text{, or approximately }549.5\text{ cm}^3}$$

Volume is always written in cubic units, such as $\text{cm}^3$, because it measures three-dimensional space.