Skill: Calculate the volume of prisms and cylinders

Volume measures the space inside a three-dimensional object. For any prism or cylinder,

$$V=Bh$$

where:

• $B$ is the area of the uniform base
• $h$ is the perpendicular height of the solid

For a cylinder, the base is a circle, so $B=\pi r^2$. Therefore,

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

Remember that the radius $r$ is half the diameter.

Example: Find the volume of a cylinder with diameter $10\text{ cm}$ and height $12\text{ cm}$. Use $\pi\approx 3.14$.

1. Find the radius.

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

2. Find the area of the circular base.

$$B=\pi r^2$$ $$B\approx 3.14(5)^2=3.14(25)=78.5\text{ cm}^2$$

3. Multiply the base area by the perpendicular height.

$$V=Bh$$ $$V\approx 78.5(12)=942\text{ cm}^3$$

The volume of the cylinder is

$$\boxed{942\text{ cm}^3}$$

For a prism, first find the area of its base—such as length $\times$ width for a rectangular prism—and then multiply by the prism’s perpendicular height. Always report volume in cubic units.