Calculating the Surface Area of a Cylinder: A Comprehensive Guide with Formula and Examples

Surface area of a Cylinder

To find the surface area of a cylinder, we need to consider two components – the area of the two circular bases and the lateral surface area

To find the surface area of a cylinder, we need to consider two components – the area of the two circular bases and the lateral surface area.

1. Area of the circular bases:
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Since a cylinder has two circular bases, the total area of the bases is 2πr^2.

2. Lateral surface area:
The lateral surface area is the curved surface area of the cylinder excluding the bases. It can be calculated by finding the area of the rectangle formed by the height of the cylinder (h) and the circumference of the circle formed by the base, which is 2πr. Thus, the lateral surface area of a cylinder is given by A = 2πrh.

Now, to find the total surface area, we add the area of the two circular bases to the lateral surface area:
Total Surface Area = Area of the bases + Lateral surface area
= 2πr^2 + 2πrh
= 2πr(r+h)

Therefore, the formula for the surface area of a cylinder is A = 2πr(r+h).

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