Geometry

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# Volume of a Hemisphere

#### Lesson Contents

## Hemisphere Volume Formula

The formula for volume of a hemisphere is given as:**V = ^{2}⁄_{3}πr^{3}**

Where

*V*is the volume and

*r*is the radius.

### When do we Need to Calculate Volume of a Hemisphere in the Real World?

There are many building structures that utilize a dome shape. Examples of these are observatories, religious buildings, and storage tanks. If one of these buildings is air conditioned, an HVAC (heating, ventilation, and air conditioning) company will need to determine how much air conditioning and heating capacity is required to control the climate inside of the building.

The company needs to know the volume inside of the building so they can properly size the air conditioning and heating units that they will install. If the dome building has hemisphere geometry, they can simply use the formula for volume of a hemisphere to find the volume of this building.

### Example Problems

**Problem 1:**

Find the volume of a hemisphere with a diameter of 10.

Solution:

1.) First, we need to find the radius. To do this, we divide 10 by 2, giving us r = 5.

2.) Now, we will plug the radius into the formula.

V = ^{2}⁄_{3}πr^{3}

V = ^{2}⁄_{3}π(5)^{3} = 261.8

3.) ** The volume is 261.8.**

**Problem 2:**

Find the volume of a hemisphere with a radius of 12.

Solution:

1.) We can directly plug the radius into the formula.

V = ^{2}⁄_{3}πr^{3}

V = ^{2}⁄_{3}π(12^{3}) = 3,619.1

2.) **The volume is ****3,619.1.**