Volume of Hemisphere

Introduction

The volume of hemisphere is the measure of the space inside half of a sphere. A hemisphere is formed when a sphere is cut into two halves along its centre. Shapes like bowls, domes, and half oranges are real-life examples of hemispheres that we find around us. 

The concept of the volume of hemisphere is useful in daily life. For example, it helps us calculate how much water a half-round tank can hold or the capacity of a bowl. Thus, understanding this concept is important both in mathematics and in the real world too.

 

Table of Contents

• Definition
• Hemisphere Equation
• Fun Facts
• Solved Problems
• Practice Questions
• Conclusion
• FAQs on Volume of Hemisphere

 

Definition

A hemisphere is half of a sphere. If we cut a round ball (sphere) into 2 equal parts, each part is called a hemisphere. It has one flat circular face and one curved surface.The volume of a hemisphere means the total space inside it, & it tells us how much a hemisphere can hold.

 

Hemisphere Equation

The formula to find the volume of hemisphere is

Volume of Hemisphere = $\frac{2}{3}\pi r ^{3}$

Where:

• r = radius (distance from the center to the edge of the sphere)

• π = 3.1416 (a fixed number used in circles and spheres)

• This formula helps us quickly calculate the space inside a hemisphere.

 

Fun Facts

• A hemisphere dome is easier to build than a full sphere dome because the shape is simpler.

• Hemisphere is often used in tanks and water reservoirs to store liquids.

• The inside of the famous Roman Pantheon looks like a giant hemisphere.

• In astronomy, the volume of a hemisphere is used to study planets and stars.

• The floating hemisphere, like buoys in the sea, remains balanced due to its round shape.

 

Solved Problems

Example 1: Basic Calculation 

Find the volume of a hemisphere of radius 7 cm.

Solution:

$Volume = \frac{2}{3} \pi r^3 \\$

${Volume} = \frac{2}{3} \times \frac{22}{7} \times 7^3 \\$

${Volume} = \frac{2}{3} \times \frac{22}{7} \times 343 \\$

${Volume} = \frac{2 \times 22 \times 343}{21} = 718.67 \, \text{cm}^3$

So, the volume is $718.67 \, \text{cm}^3$.

 

Example 2: Real-Life Bowl

A bowl is in the shape of a hemisphere with a radius of 10 cm. Find out how much space it can hold.

Solution:

$\text{Volume}= \frac{2}{3} \pi r^3 \\$

$\text{Volume}= \frac{2}{3} \times 3.1416 \times 10^3 \\$

$\text{Volume}= \frac{2}{3} \times 3.1416 \times 1000 \\$

$\text{Volume}= 2094.4 \, \text{cm}^3$

So, the bowl can hold about $2094.4 \, \text{cm}^3$.

 

Example 3: Comparing with Sphere 

The radius of the sphere is 6 cm. Find the volume of the hemisphere formed from it.

Solution:

$\text{Volume of sphere} = \frac{4}{3} \pi r^3 \\$

$\text{Volume of sphere} = \frac{4}{3} \times 3.1416 \times 6^3 \\$

$\text{Volume of sphere} = \frac{4}{3} \times 3.1416 \times 216 \\$

$\text{Volume of sphere} = 904.32 \, \text{cm}^3$

Since a hemisphere is half of a sphere:

$\text{Volume of Hemisphere } = \frac{1}{2} \times 904.32 = 452.16 \, \text{cm}^3$

 

Practice Questions

1. Find the volume of a hemisphere with radius 14 cm.

2. A dome is shaped like a hemisphere with a radius of 21 metres. Find out the volume.

3. A spherical ball of radius 12 cm is cut into two hemispheres. Find the volume of one hemisphere.

4. The volume of a hemisphere is $904.32 \, \text{cm}^3$. Find the radius.

5. The radius of a water tank in the shape of a hemisphere is 3 metres. Find the tank capacity in cubic metres.

 

Conclusion

The volume of hemisphere tells us how much space is inside half of a sphere. By using the formula $\frac{2}{3} \pi r^3 \\$, we can easily calculate this volume when the radius is known. This concept is not only important in maths but also in daily life, such as finding the capacity of bowls, domes, or tanks.

By practising solved examples and questions, you can build a clear understanding of how to apply the formulas. Remember, learning about hemispheres connects maths with the real world and helps us see how geometry is used around us.

 

Frequently Asked Questions on Volume of Hemisphere

1. What is the formula for the volume of a hemisphere?

The formula is:

Volume = $\frac{2}{3} \pi r^3 \\$

Where r is the radius of the sphere.

 

2. How do we define the volume of a hemisphere?

The volume of a hemisphere is the space inside half of a sphere. It tells us how much a hemisphere can hold.

 

3. Does the position of a hemisphere change its volume?

Even if you turn the hemisphere upside down or sideways, its volume stays the same.

 

4. Find the volume of a hemisphere with radius 7 cm.

Using the formula:

$V = \frac{2}{3} \pi r^3$

$V = \frac{2}{3} \times 3.14 \times 7^3$

$V = \frac{2}{3} \times 3.14 \times 343$

$V = 718.67 \, \text{cm}^3 \, (\text{approx.})$

 

5. What should we do if the radius is given in different units?

If the radius is in mm, cm, or m, first convert it to the same unit, then use the formula to find the volume.