Area of a Cylinder
To find the area of a cylinder, we need to consider both the curved surface area and the area of the two circular bases
To find the area of a cylinder, we need to consider both the curved surface area and the area of the two circular bases.
The formula for finding the curved surface area of a cylinder is given by:
Curved Surface Area = 2πrh
where π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.
The formula for finding the area of a circle is given by:
Area of Circle = πr²
where r is the radius of the circular base.
To find the total surface area of the cylinder, we need to add the areas of the two circular bases to the curved surface area. The formula for the total surface area of a cylinder is:
Total Surface Area = 2πrh + 2πr²
Let’s work through an example:
Suppose we have a cylinder with a radius of 5 cm and a height of 10 cm.
1. Curved Surface Area:
Curved Surface Area = 2πrh
= 2π(5)(10)
= 100π cm²
2. Area of Circular Base:
Area of Circle = πr²
= π(5)²
= 25π cm²
3. Total Surface Area:
Total Surface Area = 2πrh + 2πr²
= 2π(5)(10) + 2π(5)²
= 100π + 50π
= 150π cm²
So, the total surface area of the cylinder is 150π cm².
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