Surface area is the total area that covers the surface of a three-dimensional object. To calculate the surface area of a cylinder, you need to add the areas of the two circular bases and the lateral surface area.
The formula to calculate the surface area of a cylinder is:
Surface Area = 2πr² + 2πrh
Where:
- r is the radius of the base of the cylinder
- h is the height of the cylinder
- π is the mathematical constant pi, approximately equal to 3.14159
To calculate the surface area of a cylinder, follow these steps:
1. Measure the radius (r) and height (h) of the cylinder. Make sure they are in the same units (e.g. centimeters, inches).
2. Calculate the area of the two circular bases using the formula A = πr².
3. Calculate the lateral surface area using the formula L = 2πrh.
4. Add the areas of the two circular bases and the lateral surface area to get the total surface area of the cylinder.
For example, let's say you have a cylinder with a radius of 5 cm and a height of 10 cm. To calculate the surface area:
1. Calculate the area of the two circular bases:
A = π(5 cm)² = 25π cm²
2. Calculate the lateral surface area:
L = 2π(5 cm)(10 cm) = 100π cm²
3. Add the areas of the two circular bases and the lateral surface area:
Surface Area = 2(25π cm²) + 100π cm²
Surface Area = 50π cm² + 100π cm²
Surface Area = 150π cm²
So, the surface area of the cylinder is 150π square centimeters.
Unit 6 lesson 9 surface area cylinders
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