## Title:How to Find the Volume of a Hemisphere

-- -- --## Introduction:-

--# Listen full article:

## Explanation:-

--## What is a Hemisphere?

--## Properties of a Hemisphere:

--## Some Problems related on area of Hemisphere:

--### Question(1): The diameter of a hemisphere is 42cm, find its curved surface area.(Take π = 22/7)

Answer:

Diameter of hemisphere (d) = 42 cm

∴ Radius of hemisphere(r) = d/2

= 42/2

= 21 cm

∴ CSA of the hemisphere = 2πr²

= 2 x 22/7x 21²

= 2 x 22/7 x 21 x 21

= 2 x 22 x 3 x 21

= 2772 cm²

### Question(2):The radius of a hemisphere is 7m find its CSA.(Take π = 22/7)

Answer:

Radius (r) = 7m

∴ CSA of the hemisphere = 2πr²

= 2 x 22/7 x 7²

= 2 x 22 x 7

= 308 m²

### Question(3):The radius of a hemisphere is 10 cm,find its total surface area.(Take π = 3.14)

Answer:

Radius of the hemisphere (r)=10cm

∴ TSA of hemisphere = 3πr²

= 3 x 3.14 x 10²

= 3 x 3.14 x 100

= 3 x 314.00

= 942cm²

## Applications of Hemispheres:

--## Volume of a Hemisphere: Mathematical Foundation

## Key Variables in the Formula of Hemisphere:

--## Step-by-Step Calculation of Volume of a Hemisphere:

--## Some Problems related on Volume of Hemisphere:

### (1) Question: Find the volume of the hemisphere whose radius is 21 cm.(Take π = 22/7)

Answer:

Radius of the hemisphere (r)=21cm

∴ Volume of the hemisphere = ⅔ πr³

= ⅔ x 22/7 x (21)³

= ⅔ x 22/7 x 21 x 21 x 21

= 2 x 22 x 21 x 21

= 19404 cm³

### (2) Question: Find the radius of the hemisphere whose volume is 18π m³.

Answer:

Volume of the sphere = 18 π m³

Let, the radius of the hemisphere = r meter

A/Q,

⅔ πr³ = 18 π

=> r³ = (18π x 3) / 2π

=> r³ = 9 x 3

=> r³ = 3³

=> r = 3

∴ The radius of the hemisphere(r) = 3 m

### (3) Question: The diameter of a hemisphere is 60cm, find it’s volume.(Take π = 3.14)

Answer:

Diameter of hemisphere (d) = 60cm

∴ Radius of hemisphere(r) = d/2

= 60 /2

= 30 cm

∴ Volume of the hemisphere = ⅔ πr³

= ⅔ x 3.14 x 30³

= ⅔ x 3.14 x 27000

= 2 x 3.14 x 9000

= 56520 cm³

## Visualizing a Hemisphere:

--## Comparing the Volume of a Hemisphere to Other Shapes:

## Comparative Analysis:-

--## Common Mistakes When Calculating Volume of a Hemisphere:

## Real-World Applications of Volume Calculations:-

--## Conclusion:-

# FREQUENTLY ASKED QUESTIONs ON VOLUME OF HEMISPHERE:

(a). What is hemisphere class 9?

+Answer: A hemisphere is defined as half of a sphere, which is divided by a plane passing through its center. It can be thought of as the upper or lower half of a sphere. The term “hemisphere” comes from the Greek word “hemisphairion,” meaning "half a sphere."

(b). How to find the volume of a hemisphere with diameter

+Answer:∵ Radius of hemisphere(r)= d/2

where, d is the diameter of hemisphere

Now,

Volume of hemisphere = ⅔ πr³

= ⅔ π(d/2)³

= ⅔ πd³/8

= (1/12) πd³

(c). What is the volume and SA of a hemisphere?

+Answer:Volume of hemisphere = ⅔ πr³

where r = radius of the hemisphere

and

SA of a hemisphere = CSA of hemisphere + Area of its base

= 2πr² + πr²

= 3πr², where, r = Radius of the hemisphere.

(d). What is a hemisphere in maths?

+Answer:In maths, a hemisphere is defined as half of a sphere, which is divided by a plane passing through its center. It can be thought of as the upper or lower half of a sphere.

(e).What is the volume of a hollow hemisphere Class 10?

+Answer:The volume of a hollow hemisphere = ⅔ π(R³- r³)

where, R = Outer radius of sphere

and r = Inner radius of hemisphere.