Surface area of a Cylinder
To find the surface area of a cylinder, we need to calculate the sum of the areas of its curved surface and its two circular bases
To find the surface area of a cylinder, we need to calculate the sum of the areas of its curved surface and its two circular bases.
1. Curved Surface Area:
The curved surface of a cylinder can be thought of as a rectangle that has been wrapped around the cylinder. The length of this rectangle is equal to the height (h) of the cylinder, and the width is equal to the circumference (C) of the circular base.
The formula for the circumference (C) of a circle is given by C = 2πr, where r is the radius of the base. Since the rectangle is wrapped around the cylinder once, its length is equal to the height of the cylinder.
Therefore, the curved surface area (CSA) is given by:
CSA = C * h = 2πr * h, where r is the radius of the base and h is the height of the cylinder.
2. Area of Circular Bases:
The area of each circular base is given by the formula A = πr^2, where r is the radius of the base.
Therefore, the total area of both circular bases (A_base) is given by:
A_base = 2 * πr^2, where r is the radius of the base.
3. Total Surface Area:
To find the total surface area (TSA) of the cylinder, we add the curved surface area (CSA) to the area of both circular bases (A_base).
TSA = CSA + A_base
TSA = 2πr * h + 2πr^2
TSA = 2πr (r + h)
So, the formula for the surface area of a cylinder is TSA = 2πr (r + h), where r is the radius of the base and h is the height of the cylinder.
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