Curved Surface Area and Total Surface Area of Cylinders
A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface. Calculating its surface area involves determining the area of both the curved surface and the two circular bases.
Curved Surface Area
The curved surface area of a cylinder is calculated using the formula: 2πrh, where 'r' represents the radius of the circular base and 'h' represents the height of the cylinder. The value of π (pi) is approximately 3.14159.
Area of Circular Bases
Each circular base of the cylinder has an area calculated using the formula: πr². Since there are two bases, the total area of both bases is 2πr².
Total Surface Area
The total surface area of a cylinder is the sum of the curved surface area and the area of the two circular bases. Therefore, the formula for the total surface area is: 2πrh + 2πr². This can be simplified to 2πr(r + h).
Units of Measurement
Consistent units of measurement must be used throughout the calculation. For example, if the radius is measured in centimeters, the height must also be in centimeters. The resulting surface area will then be in square centimeters (cm²).
Example Calculation
Consider a cylinder with a radius (r) of 5 cm and a height (h) of 10 cm.
- Curved surface area: 2πrh = 2 3.14159 5 cm 10 cm ≈ 314.16 cm²
- Area of bases: 2πr² = 2 3.14159 (5 cm)² ≈ 157.08 cm²
- Total surface area: 314.16 cm² + 157.08 cm² ≈ 471.24 cm²