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# Area of Hemisphere (Curved and Total Surface Area)| Formulas

## Hemisphere Definition

Hemispheres are three-dimensional objects that are often used in mathematics and science. A hemisphere is half of a sphere, and it is a special case of a spherical cap, which is the portion of a sphere that lies above or below a plane. In this article, we will explore hemispheres in detail and explain their properties, formulas, and applications.

## What is the Surface Area of Hemisphere?

A hemisphere is a three-dimensional shape that is half of a sphere. To find the surface area of a hemisphere, we need to add up the areas of all its faces.

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

Surface Area = 2πr²

Where r is the radius of the hemisphere and π is the mathematical constant pi, approximately equal to 3.14159.

For example, if the radius of a hemisphere is 5 cm, the surface area would be:

Surface Area = 2π(5 cm)²

2π(25 cm²)

Surface Area = 50π cm²

Therefore, the surface area of a hemisphere with a radius of 5 cm is approximately 50π cm².

## Surface Area of a Hemisphere Formula

The surface area is divided into two types, which is giver here;

• Curved Surface Area (CSA)
• Total Surface Area (TSA)

### Curved Surface Area

The curved surface area of a hemisphere is the surface area of the dome-shaped curved surface of the hemisphere, not including the flat circular base. To calculate the curved surface area of a hemisphere, we can use the formula:

Curved Surface Area = 2πr²

where “r” is the radius of the hemisphere and “π” is the mathematical constant pi, approximately equal to 3.14159.

For example, if the radius of a hemisphere is 5 cm, the curved surface area would be:

Curved Surface Area = 2π(5 cm)²

= 2π(25 cm²)

Curved Surface Area = 50π cm²

### Total Surface Area (TSA)

The total surface area of a hemisphere is the sum of the area of its curved surface and the area of its flat circular base. To calculate the total surface area of a hemisphere, we can use the formula:

Total Surface Area (TSA) = Curved Surface Area + Area of the Base Circle

= 2πr² + πr²

= 3πr²

where “r” is the radius of the hemisphere and “π” is the mathematical constant pi, approximately equal to 3.14159.

The first term, 2πr², represents the area of the curved surface of the hemisphere, while the second term, πr², represents the area of the circular base.

For example, if the radius of a hemisphere is 5 cm, the total surface area would be:

Total Surface Area (TSA) = Curved Surface Area + Area of the Base Circle

= 3πr²

Total Surface Area = 3π(5 cm)²

= 3π(25 cm²)

Total Surface Area = 75π cm²

## How to Find the Surface Area of a Hemisphere?

Here are we’ll explain how to find the area of a hemisphere step-by-step.

##### Step 1: Understand the Formula

The formula for the surface area of a hemisphere is:

Surface Area = 2 x π x r^2

where r is the radius of the hemisphere.

##### Step 2: Determine the Radius

To find the area of a hemisphere, you first need to determine the radius of the sphere. The radius is the distance from the center of the sphere to its edge. Measure the radius with a ruler or use a known value.

##### Step 3: Square the Radius

Once you have the radius, square it by multiplying it by itself. For example, if the radius is 5 cm, then 5^2 = 25.

##### Step 4: Multiply by π

Next, multiply the squared radius by π (pi). Pi is a mathematical constant that represents the ratio of a circle’s circumference to its diameter and is approximately 3.14159. Continuing the example, 25 x π = 78.54.

##### Step 5: Multiply by 2

Finally, multiply the result from Step 4 by 2 to get the surface area of the hemisphere. In this example, 78.54 x 2 = 157.08. Therefore, the surface area of a hemisphere with a radius of 5 cm is approximately 157.08 square centimeters.

### Examples on Area of Hemisphere

##### Example 1: Find the total surface area of a hemisphere with a radius of 4 cm.

Solution: We can use the formula for the total surface area of a hemisphere, which is:

Total Surface Area = 2πr² + πr²

pi approximately equal to 3.14159.

we get:

Total Surface Area = 2π(4 cm)² + π(4 cm)²

= 2π(16 cm²) + π(16 cm²)

= 32π cm² + 16π cm²

Total Surface Area = 48π cm²

##### Example 2: Find the curved surface area of a hemisphere with a radius of 3.5 cm.

Solution: We can use the formula for the curved surface area of a hemisphere, which is:

Curved Surface Area = 2πr²

where “r” is the radius of the hemisphere and “π” is the mathematical constant pi, approximately equal to 3.14159.

Curved Surface Area = 2π(3.5 cm)²

= 2π(12.25 cm²)

Curved Surface Area = 24.5π cm²

## Frequently Asked Questions on Area of Hemisphere

Q: What is a hemisphere?

A: A hemisphere is a half-sphere, or a three-dimensional object that is shaped like a dome. It is a solid figure that is created by rotating a semicircle around its diameter.

Q: What is the formula for the total surface area of a hemisphere?

A: The formula for the total surface area of a hemisphere is 2πr² + πr², where “r” is the radius of the hemisphere and “π” is the mathematical constant pi, approximately equal to 3.14159.

Q: What is the formula for the curved surface area of a hemisphere?

A: The formula for the curved surface area of a hemisphere is 2πr², where “r” is the radius of the hemisphere and “π” is the mathematical constant pi, approximately equal to 3.14159.

Q: What is the formula for the area of the flat circular base of a hemisphere?

A: The formula for the area of the flat circular base of a hemisphere is πr², where “r” is the radius of the hemisphere and “π” is the mathematical constant pi, approximately equal to 3.14159.

Q: What units are used to measure the area of a hemisphere?

A: The area of a hemisphere is usually measured in square units, such as square centimeters or square meters.

Q: What are some real-world applications of the area of a hemisphere?

A: The area of a hemisphere is used in many real-world applications, such as in architecture, engineering, and physics. For example, the area of a dome can be used to calculate the amount of roofing material needed to cover it, or the area of a tank can be used to determine its capacity.