Surface Area of Hemisphere Calculator

To calculate the surface area of a hemisphere, square the radius, multiply by π (3.14159), and then multiply the result by 3. This formula gives the total surface area, which includes both the curved surface and the flat circular base.

Surface Area of Hemisphere Calculator

Enter any 1 value to calculate the missing variable

Radius

Inches Feet Centimeters Meters

Surface Area

sq in sq ft sq cm sq m

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The Surface Area of Hemisphere Calculator calculates the total surface area of a hemisphere based on its radius. By using the formula $SA = 3\pi r^2$ this tool provides an easy way to determine the surface area for both curved and flat surfaces of the hemisphere.

Formula:

The surface area of a hemisphere can be calculated using the formula:

$$SA = 2\pi r^2 + \pi r^2 = 3\pi r$$

Where:

• SA = Total surface area of the hemisphere
• r = Radius of the hemisphere

The formula accounts for:

• 2πr²: The curved surface area of the hemisphere.
• πr²: The flat circular base of the hemisphere.

Variable	Description
SA	Surface area of the hemisphere
r	Radius of the hemisphere
π	Pi (approximately 3.14159)

Example Calculation:

Let’s assume the radius (r) of the hemisphere is 10 cm.

Using the formula:

$$SA = 3\pi(10)^2 = 3\pi(100) = 300\pi \approx 300 \times 3.14159 = 942.48 \, \text{cm}^2$$

So, the total surface area of the hemisphere is approximately 942.48 cm².

Step	Calculation	Result
1	Square the radius: $10^2 = 100$	100
2	Multiply by 3 and π: $3 \times 3.14159 \times 100$	942.48 cm²

What is Surface Area of Hemisphere Calculator ?

The Surface Area of a Hemisphere Calculator helps determine the total surface area of a hemisphere, which consists of both the curved surface and the flat circular base. To calculate the surface area of a hemisphere, you need to use the following concepts: the curved surface area and the total surface area.

The curved surface area of a hemisphere is half the surface area of a full sphere, which is given by $2\pi r^2$ where r is the radius. The total surface area includes both the curved surface and the area of the circular base, resulting in the formula $3\pi r^2$.

You can use a surface area of hemisphere calculator to automate this calculation, especially for larger or more complex problems. The tool is helpful when calculating the surface area of objects in real-world scenarios, such as domes or containers shaped like hemispheres.

Additionally, understanding the lateral surface area of a hemisphere, which excludes the base, is useful when only the curved part of the hemisphere is needed. Tools like the surface area of a hemisphere without base or curved surface area calculator help in such cases.