Surface Area of Cylinders

As with a rectangular prism, the surface area of a cylinder is the sum of the areas of all its surfaces. In the case of a cylinder, the top and bottom (or bases) are circles, and the curved surface is a rectangle whose length is equal to the circumference of the circle at its base. Use the slides below to learn how to find the surface area of a cylinder.

Find the surface area of a can of cat food with a diameter of 8.6 centimeters and a height of 4.4 centimeters.

A perspective view of the can would look like this:

Cylinder with diameter of 8.6 cm and height of 4.4 cm

Find the surface area of a can of cat food with a diameter of 8.6 centimeters and a height of 4.4 centimeters.

A net of the can would look like this:

Diagram of the surface area of a cylinder

Find the surface area of a can of cat food with a diameter of 8.6 centimeters and a height of 4.4 centimeters.

Let’s begin by finding the area of the rectangle that represents the curved surface. To do this, we first need to find the circumference of the circle that makes up the base of the cylinder. The formula for the circumference of a circle is C = πd. The diameter of the base is 8.6 cm, so the circumference of the base is 27 cm.

C = (3.14)(8.6) = 27.004 ≈ 27

The area of the rectangle will be the circumference of the base times the height of the can, or 118.8 square centimeters.

A = C × h
A = (27)(4.4) = 118.8

Find the surface area of a can of cat food with a diameter of 8.6 centimeters and a height of 4.4 centimeters.

To find the area of each base, we will need to find the radius of the circle.

r = d ÷ 2 = 8.6 ÷ 2 = 4.3

To find the area of one base, we will find the area of a circle whose radius is 4.3 centimeters using the circle area formula, A = πr².

A = (3.14)(4.3²)

Substitute the values of π and r.

A = (3.14)(18.49)

Square the radius.

A = 58.0586 ≈ 58.1

Multiply and round to the nearest tenth.

Find the surface area of a can of cat food with a diameter of 8.6 centimeters and a height of 4.4 centimeters.

The area of one base is 58.1 square centimeters. Each base is the same size, so the area of the two bases together is 116.2 square centimeters.

(58.1)(2) = 116.2

Find the surface area of a can of cat food with a diameter of 8.6 centimeters and a height of 4.4 centimeters.

The total surface area of the can of cat food is the sum of the area of the curved surface and the area of the two bases.

SA = 118.8 + 116.2 = 235

The surface area of the can is 235 square centimeters (or 235 cm²).

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Surface Area of Cylinders

How do you find the surface area of a curved object?