Calculate the volume of cylinders

Volume of a cylinder is understood as the amount of three-dimensional space it occupies, calculated by multiplying the area of its circular base, $\pi r^2$ , by its perpendicular height: $V=\pi r^2h$ . Learners distinguish radius from diameter, select consistent linear units, express volume in cubic units, and interpret exact or appropriately rounded values; more advanced treatments involving oblique or variable-radius cylinders are outside this scope.

Detailed Explanation: 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.

Learn by doing: Calculate the volume of cylinders

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Volume - Cylinder - Image to Decimal

Earned ?

Calculate the volume of cylinders

Detailed Explanation: Calculate the volume of cylinders

Learn by doing: Calculate the volume of cylinders

Practice with unlimited practice problems

Practice:

Volume - Cylinder - Image to Decimal