Skill: Calculate the volume of cylinders

A cylinder has two circular bases. To find its volume, find the area of one circular base and multiply by the cylinder’s perpendicular height:

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

Here:

• $r$ is the radius of the circular base.
• $h$ is the height of the cylinder.
• Volume is written in cubic units, such as $\text{cm}^3$ or $\text{m}^3$.

If the problem gives the diameter, divide it by $2$ to find the radius.

Example: Find the volume of a cylinder with a diameter of $10\text{ cm}$ and a height of $12\text{ cm}$.

Step 1: Find the radius.

The radius is half the diameter:

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

Step 2: Substitute into the formula.

$$V=\pi r^2h$$ $$V=\pi(5)^2(12)$$

Step 3: Calculate.

$$V=\pi(25)(12)=300\pi\text{ cm}^3$$

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

$$V\approx300(3.14)=942\text{ cm}^3$$

So, the volume is

$$\boxed{300\pi\text{ cm}^3\approx942\text{ cm}^3}$$

Always make sure the radius and height use the same units, and express the final answer in cubic units.