Surface Area of a Cylinder Calculator
A surface area of a cylinder calculator helps compute the total area covering the exterior of a cylindrical object by taking into account both the circular bases and the curved lateral surface of the cylinder.
You're tasked with painting a large cylindrical water tank. To estimate the amount of paint needed, you'd need to calculate its surface area. Let's say the tank has a radius of 3 meters and a height of 10 meters. Using the calculator, you'd input these dimensions and quickly obtain the total surface area, which in this case would be approximately 245.04 square meters.Surface Area of a Cylinder Calculation Chart
| Component | Formula | Calculation | Result |
|---|---|---|---|
| Lateral Surface Area | 2πrh | 2 × π × 3 × 10 | 188.50 m² |
| Area of Two Circular Bases | 2πr² | 2 × π × 3² | 56.55 m² |
| Total Surface Area | 2πrh + 2πr² | 188.50 + 56.55 | 245.04 m² |
| Lateral Surface Area | 2πrh | 2 × π × 5 × 15 | 471.24 cm² |
| Area of Two Circular Bases | 2πr² | 2 × π × 5² | 157.08 cm² |
| Total Surface Area | 2πrh + 2πr² | 471.24 + 157.08 | 628.32 cm² |
| Lateral Surface Area | 2πrh | 2 × π × 7 × 20 | 871.57 m² |
| Area of Two Circular Bases | 2πr² | 2 × π × 7² | 307.76 m² |
| Total Surface Area | 2πrh + 2πr² | 871.57 + 307.76 | 1179.33 m² |
| Lateral Surface Area | 2πrh | 2 × π × 4 × 12 | 301.59 m² |
| Area of Two Circular Bases | 2πr² | 2 × π × 4² | 100.53 m² |
| Total Surface Area | 2πrh + 2πr² | 301.59 + 100.53 | 402.12 m² |
Cylinder with Radius 7 m and Height 20 m:
Lateral Surface Area: 2πrh = 2 × π × 7 × 20 = 871.57 m²
Area of Two Bases: 2πr² = 2 × π × 7² = 307.76 m²
Total Surface Area: 871.57 + 307.76 = 1179.33 m²
Cylinder with Radius 4 m and Height 12 m:
Lateral Surface Area: 2πrh = 2 × π × 4 × 12 = 301.59 m²
Area of Two Bases: 2πr² = 2 × π × 4² = 100.53 m²
Total Surface Area: 301.59 + 100.53 = 402.12 m²
Surface Area of a Cylinder Formula
The formula for calculating the surface area of a cylinder is:
A = 2πrh + 2πr²Where:
- A is the total surface area
- π (pi) is approximately 3.14159
- r is the radius of the circular base
- h is the height of the cylinder
This formula combines two components:
2πrh: represents the lateral surface area (curved side)
2πr²: accounts for the area of both circular bases
Let’s use example of the water tank (radius 3m, height 10m):
Lateral surface area: 2π × 3 × 10 = 188.50 m²
Area of two bases: 2π × 3² = 56.55 m²
Total surface area: 188.50 + 56.55 = 245.04 m²
What is the Surface Area of the Given Cylinder?
Let’s consider a different cylinder with a radius of 5 cm and a height of 15 cm. We’ll calculate its surface area step by step:
Lateral surface area: 2πrh = 2 × π × 5 × 15 = 471.24 cm²
Area of two bases: 2πr² = 2 × π × 5² = 157.08 cm²
Total surface area: 471.24 + 157.08 = 628.32 cm²
The surface area of this cylinder is approximately 628.32 square centimeters.
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