Calculating the Surface Area of a Cylinder: Formula and Example

Area of a Cylinder

To calculate the area of a cylinder, we need two measurements – the radius of the circular base (r) and the height of the cylinder (h)

To calculate the area of a cylinder, we need two measurements – the radius of the circular base (r) and the height of the cylinder (h).

The formula to calculate the surface area of a cylinder is:
A = 2πrh + 2πr^2

Let’s break down each term in the formula:

1. Base area (2πr^2):
The base area is the area of the two circular bases of the cylinder. Since a cylinder has two bases, we multiply the area of one base by 2. The formula for the area of a circle is A = πr^2, where r is the radius. Therefore, the base area of a cylinder is 2πr^2.

2. Lateral area (2πrh):
The lateral area is the area of the curved surface of the cylinder. It can be thought of as a rectangle that has been rolled up to form a tube. The length of this rectangle is the circumference of the base, which is 2πr, and the height of the rectangle is the height of the cylinder (h). Therefore, the lateral area of a cylinder is 2πrh.

To find the total surface area (A), we add the base area and the lateral area:

A = 2πrh + 2πr^2

This formula can be simplified by factoring out 2πr:

A = 2πr(h + r)

Now, let’s work through an example:

Example:
Find the surface area of a cylinder with a radius of 4 cm and a height of 10 cm.

Solution:
Using the formula A = 2πrh + 2πr^2, we substitute r = 4 cm and h = 10 cm:

A = 2π(4)(10) + 2π(4)^2
A = 80π + 32π
A = 112π

So, the surface area of the given cylinder is 112π square centimeters.

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