Calculate the volume of cylinders

Volume of a cylinder is the amount of three-dimensional space it occupies, found by multiplying the area of its circular base by its perpendicular height: $V=\pi r^{2}h$ . This includes interpreting radius and diameter correctly, selecting consistent linear units, expressing the result in cubic units, and using $\pi$ as an exact value or an appropriate approximation; more advanced work with variable formulas, composite solids, or nonstandard cylinders is not included.

Detailed Explanation: 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.

Learn by doing: Calculate the volume of cylinders

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Volume of a Cylinder - Calculate

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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

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Volume of a Cylinder - Calculate