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How to Find Surface Area and Volume of a Cylinder

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Now you’ll learn how to calculate the surface area and volume of a cylinder. Let’s start by once again going over what a cylinder is. A cylinder is a tube where the top and bottom are circles or ellipses.

For these examples, you will only work with cylinders with circular bases. Remember, the top and the bottom—the two bases—are always identical.

Cylinder Surface are of a cylinder

Surface Area

From the figure above you can see that the surface area of a cylinder consists of the area of two circles or ellipses and one rectangle.

Formula

Surface Area of a Cylinder

A = 2 \cdot π r^{2} + 2 π r \cdot h

The first term in the formula is the area of the circles, and the second term is the area of the rectangle. The length of the rectangle is the circumference of the circle.

Example 1

Calculate the surface area of a cylinder with height of $7 cm$ and a radius of $4 cm$ :

A = 2 \cdot π \cdot 4^{2} + 2 \cdot π \cdot 4 \cdot 7 \approx 276.32 {cm}^{2}

Example 2

Calculate the surface area of a cylinder with height that equals $4 cm$ and a diameter of $6 cm$ :

You must first find the radius of the bases, which is half their diameter:

\begin{array}{l} r & = \frac{6}{2} = 3 \\ A & = 2 \cdot π \cdot 3^{2} + 2 \cdot π \cdot 3 \cdot 4 \\ \approx 131.88 {cm}^{2} \end{array}

\begin{matrix} r = \frac{6}{2} = 3 \\ A = 2 \cdot π \cdot 3^{2} + 2 \cdot π \cdot 3 \cdot 4 \approx 131.88 {cm}^{2} \end{matrix}

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Volume

When calculating the volume of a cylinder, multiply the area of the base by the height of the cylinder.

Formula

Volume of a Cylinder

V = π r^{2} \cdot h,

where $r$ is the radius of the base, and $h$ is the height of the cylinder.

Example 3

Calculate the volume of a cylinder with a base with radius $3 cm$ and a height of $5 cm$ :

V = π \cdot 3^{2} \cdot 5 \approx 141.3 {cm}^{3}

Example 4

Calculate the volume of the cylinder with a base with radius $6 cm$ and a height of $8 cm$ :

V = π \cdot 6^{2} \cdot 8 \approx 904.32 {cm}^{3}

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What Does a Cylinder Shape Look Like?

What Does a Prism Shape Look Like?

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