Calculating the Total Surface Area of a Cylinder: Explanation and Example

Area of a Cylinder

The formula to find the area of a cylinder is A = 2πr(r+h), where A is the total surface area, r is the radius of the circular base, and h is the height of the cylinder

The formula to find the area of a cylinder is A = 2πr(r+h), where A is the total surface area, r is the radius of the circular base, and h is the height of the cylinder.

To understand the formula, let’s break it down into different parts:

1. The base of the cylinder is a circle, and the formula for the area of a circle is simply A = πr^2. This accounts for the area of the top and bottom circular bases, so we multiply it by 2 to account for both.

2. The curved surface area of the cylinder is the area of the rectangle that wraps around the cylinder. This rectangle can be “unwrapped” and flattened into a flat sheet. The length of the rectangle is the circumference of the circular base, which is 2πr, and the width is the height of the cylinder, h. So, the formula for the area of the curved surface is 2πrh.

Now, if we add the areas of the two circular bases (2πr^2) and the curved surface (2πrh), we get the total surface area of the cylinder, which is A = 2πr(r+h).

Let’s consider an example to illustrate the calculation of the area of a cylinder:

Suppose we have a cylinder with a radius of 5 units and a height of 10 units. To find the area, we can substitute these values into the formula:

A = 2πr(r+h)
A = 2π(5)(5+10)
A = 2π(5)(15)
A = 150π square units

Therefore, the area of the given cylinder is 150π square units.

Remember to always consider the units when expressing the area, as it is in square units.

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