This surface area of a cylinder calculator uses the A = 2πr² + 2πrh formula to to compute the total surface area of a cylindrical object.
For example, a cylinder with a radius of 5 cm and a height of 10 cm:
- Input: Radius = 5 cm, Height = 10 cm
- The calculator processes these values using the surface area formula.
- Output: Total surface area ≈ 471.24 cm².
The calculator typically requires input of the cylinder’s dimensions, such as its radius (or diameter) and height. Once these measurements are provided, it automatically applies the appropriate formula to calculate the total surface area.
Surface Area of a Cylinder Calculator
| Radius | Height | Total Surface Area | Curved Surface Area | Volume | Conversion |
|---|---|---|---|---|---|
| 2 cm | 5 cm | 87.96 cm² | 62.83 cm² | 62.83 cm³ | 0.00880 m² |
| 1.5 in | 4 in | 51.84 in² | 37.70 in² | 28.27 in³ | 0.0334 m² |
| 0.5 m | 2 m | 7.85 m² | 6.28 m² | 1.57 m³ | 7.85 m² |
| 10 ft | 15 ft | 1,570.80 ft² | 942.48 ft² | 4,712.39 ft³ | 145.93 m² |
| 20 cm | 30 cm | 6,283.19 cm² | 3,769.91 cm² | 37,699.11 cm³ | 0.628 m² |
Conversion equation used: 1 m² = 10.7639 ft² = 10,000 cm² = 1,550 in².
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Surface Area of a Cylinder Formula
The formula for calculating the surface area of a cylinder is:
A = 2πr² + 2πrh
Where:
- 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 can be broken down into two parts:
- 2πr²: This represents the area of the two circular bases (top and bottom).
- 2πrh: This represents the area of the curved lateral surface.
Let’s work through an example:
Consider a cylinder with a radius of 3 meters and a height of 5 meters.
- Calculate the area of the circular bases: $$2πr² = 2 × π × 3² ≈ 56.55 m²$$
- Calculate the area of the curved surface: $$2πrh = 2 × π × 3 × 5 ≈ 94.25 m²$$
- Sum these values to get the total surface area: $$56.55 m² + 94.25 m² ≈ 150.80 m²$$
The total surface area of this cylinder is approximately 150.80 square meters.
How can you find the surface area of a cylinder?
To find the surface area of a cylinder, follow these steps:
- Measure the radius: Determine the radius of the circular base. If you have the diameter, divide it by 2 to get the radius.
- Measure the height: Measure the distance between the two circular bases.
- Apply the formula: Use the formula $$A = 2πr² + 2πrh$$, where A is the surface area, r is the radius, and h is the height.
- Calculate: Plug in the values and compute the result. Remember to keep track of your units!
- Round as needed: Depending on the required precision, round your answer appropriately.
How to calculate the surface area of a tube?
The formula is:
A = 2π(r₁² – r₂²) + 2πh(r₁ + r₂)
Where:
- r₁ is the outer radius
- r₂ is the inner radius
- h is the height of the tube
For example, if a tube has an outer radius of 5 cm, an inner radius of 4 cm, and a height of 10 cm:
- $$A = 2π(5² – 4²) + 2π × 10 × (5 + 4)$$
- $$A ≈ 2π(25 – 16) + 2π × 10 × 9$$
- $$A ≈ 56.55 + 565.49$$
- $$A ≈ 622.04 cm²$$
A tube is essentially a hollow cylinder. To calculate its surface area, you need to consider both the inner and outer surfaces.
How do you find the height of a cylinder?
If you know the surface area and radius of a cylinder, you can find its height using this rearranged formula:
h = (A – 2πr²) / (2πr)
Where A is the total surface area and r is the radius.
For instance, if a cylinder has a surface area of 300 cm² and a radius of 5 cm:
- $$h = (300 – 2π × 5²) / (2π × 5)$$
- $$h ≈ (300 – 157.08) / 31.42$$
- $$h ≈ 4.55 cm$$
How to figure out the volume of a cylinder?
The formula for a cylinder’s volume is:
V = πr²h
Where r is the radius and h is the height.
For a cylinder with radius 3 cm and height 8 cm:
- $$V = π × 3² × 8$$
- $$V ≈ 226.19 cm³$$
While not directly related to surface area, the volume of a cylinder is often needed alongside surface area calculations.
Surface area of cylinder with diameter
For a cylinder with diameter 10 cm and height 15 cm:
- Radius = $$10 / 2 = 5 cm$$
- $$A = 2π × 5² + 2π × 5 × 15$$
- $$A ≈ 157.08 + 471.24$$
- $$A ≈ 628.32 cm²$$
If you’re given the diameter instead of the radius, simply divide the diameter by 2 to get the radius, then proceed with the standard formula.
Surface area of cylinder with steps
Here’s a step-by-step breakdown for finding the surface area of a cylinder with radius 4 m and height 6 m:
- Calculate the area of one circular base: $$πr² = π × 4² ≈ 50.27 m²$$
- Multiply by 2 for both bases: $$2 × 50.27 ≈ 100.54 m²$$
- Calculate the area of the curved surface: $$2πrh = 2π × 4 × 6 ≈ 150.80 m²$$
- Sum the results: $$100.54 + 150.80 = 251.34 m²$$
The total surface area is approximately 251.34 square meters.
Surface area of cylinder square feet
For a cylinder with radius 2 ft and height 5 ft:
- $$A = 2π × 2² + 2π × 2 × 5$$
- $$A ≈ 25.13 + 62.83$$
- $$A ≈ 87.96 sq ft$$
When working in square feet, ensure all measurements are in feet before applying the formula.
Surface area of cylinder square meters
Consider a cylinder with radius 1.5 m and height 3 m:
- $$A = 2π × 1.5² + 2π × 1.5 × 3$$
- $$A ≈ 14.14 + 28.27$$
- $$A ≈ 42.41 m²$$
For calculations in square meters, use measurements in meters.
Curved surface area of cylinder
The formula is:
Curved Surface Area = 2πrh
For a cylinder with radius 3 cm and height 7 cm:
- Curved Surface Area = $$2π × 3 × 7$$
- Curved Surface Area ≈ 131.95 cm².
The curved surface area (also known as lateral surface area) is the area of just the curved side of the cylinder, excluding the circular bases.
Lateral surface area of a cylinder
Using the same formula as above:
For a cylinder with radius 5 m and height 10 m:
- Lateral Surface Area = $$2π × 5 × 10$$
- Lateral Surface Area ≈ 314.16 m².
The lateral surface area is synonymous with the curved surface area. It represents the “wrap” around the cylinder, excluding the top and bottom.
