Volume of a Sphere

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Volume of a Sphere – Introduction

Have you ever wondered, “I can draw a circle, but I cannot draw a sphere? Why?” This is because a circle is a two-dimensional figure and does not have volume, whereas a sphere is a three-dimensional shape with no edges or vertices. That means its points lie in space. Hence, you cannot draw it. This is the reason we always find the volume of a sphere to calculate the amount of space it occupies. 

Scroll ahead to learn about the volume of a sphere formula, the derivation of the sphere volume formula, some solved examples, facts, and more.

What Is the Volume of a Sphere?

Volume and surface area of a sphere and a hemisphere

Wondering how we can find the volume of a sphere? Hold on, we will get to that, but first, understand what the volume of a sphere means. The volume of a sphere is the measure of three-dimensional space occupied by a sphere. It depends on the sphere’s radius, which is half the diameter (the longest line inside the sphere that passes through the center of the sphere). 

That means if the radius of the sphere changes, its volume changes too!

The volume of a sphere is measured in cubic units, such as m3, cm3, and so on.

What Is the Formula to Find the Volume of a Sphere?

How do you find the volume of a sphere given that “r” is the radius of the sphere? The volume of a sphere equation is as follows:

The volume of a sphere =43πr3

How to Calculate the Volume of a Sphere?

Suppose the radius of the sphere is 6 cm, then its volume will be:

As we know, the volume of the sphere, V =43πr3

Here, r=6 cm

Thus, volume of sphere, V =43πr3=43×3.14×6×6×6 

V =904.32cm3

Therefore, the volume of a sphere is 904.32 cm3

Volume of Solid Sphere

If the radius of the solid sphere is r, the volume of the sphere is given by:

Volume of Sphere, V =43πr3

Volume of Hollow Sphere

Sphere that has a cavity or space inside is called a hollow sphere. 

Let the radius of the outer sphere is R and the radius of the inner sphere is r. 

The volume of the sphere, V is given by:

Volume of Sphere, V = Volume of Outer Sphere – Volume of Inner Sphere 

=43πR343r3

=43π(R3r3)

Fun Facts about Spheres

How about some fun and interesting facts about the sphere? Let’s take a look!

  1. A sphere is symmetrical and round. It does not have any faces, corners, or edges.
  2. Balls, marbles, and even Earth are shaped like spheres.
  3. A hemisphere is an exact half of a sphere.
  4. All the sphere’s surface points are the same distance “r” from the center.
  5. The sphere appears in nature when a surface wants to be as small as possible. For example, if you blow up a balloon, it naturally forms a sphere!

Conclusion

So, how was the lesson? We hope you have got a clear understanding of the volume of spheres. Stay tuned with SplashLearn for more useful math lessons like these.

Solved Examples

1. What is the volume of a sphere with a radius of 12 units?

Solution: To solve for the volume of a sphere, you must first know the equation for the volume of a sphere.

The equation for the volume of a sphere is:

V =43πr3

If the radius of the sphere is 12, then you plug that in for r and solve:

V =43πr3=43×3.14×12×12×12=7234.56 cubic units 

2. Find the volume of the sphere whose diameter is 28 cm.

Solution: Given, diameter =28cm

So, radius =Diameter2=282=14cm

From there, we can use the formula, which is

V =43πr3=43×3.14×14×14×14=11488.23cm3

3. Find the volume of a spherical tank whose radius is 3 inches.

Solution:

The equation for the volume of a sphere is:

V =43πr3

If the radius of the sphere is 3 inches, then you plug that in for r and solve:

V =43πr3=43×3.14×3×3×3=113.04 cubic inches 

4. Nina created a spherical ball of radius 5 cm using clay. She then cut the sphere into two equal parts. What will be the volume of each part?

Solution:

The equation for the volume of a sphere is:

V =43πr3

If the radius of the sphere is 5 cm, then you plug that in for r and solve:

V =43πr3=433.14555=523.33 cm3

Hence volume of each cut part =523.332=261.66 cm3

5.  Sam wants to create a sphere of radius 7 cm using some clay. What will be the volume of the sphere formed?

Solution:

The equation for the volume of a sphere is:

V =43πr3

If the radius of the sphere is 7 cm, then you plug that in for r and solve:

V =43πr3=43×3.14×7×7×7=1436.02 cm3

Practice Problems

Volume of a Sphere

Attend this quiz & Test your knowledge.

1

What is the volume of the sphere, whose radius is 4 units?

88.3π
77.3π
85.3π
90π
CorrectIncorrect
Correct answer is: 85.3π
To solve for the volume of a sphere, you must first know the equation for the volume of a sphere. The equation is V =43πr3 Then plug the radius into the equation for r, yielding V =43×π×4×4×4=85.3π
2

Find the volume of a sphere of radius 10 cm.

4186.66cm3
2186.66cm3
4189.66cm3
41.66cm3
CorrectIncorrect
Correct answer is: 4186.66cm3
The volume of the sphere = V =43πr3=43×3.14×10×10×10=4186.66cm3
3

A spherical-shaped tank has a radius of 21 m. Now find the capacity of it in liters to store water in it.

28,808,000 liters
38,808,000 liters
38,888,000 liters
30,808,000 liters
CorrectIncorrect
Correct answer is: 38,808,000 liters
The given values are,
r =21 m
Now the volume of a sphere,
V =43×π×r3
V =43×21×21×21
V =4×22×21×21
V =38808 m3
Since,
1m3=1000 liter
Then the capacity of the tank,
=38,808m3×1000
=38,808,000 liter
So, 38,808,000 liters of water can be stored in the tank.
4

The volume of the sphere is 2100cm3. What is the radius of the hemisphere formed by cutting the sphere into two equal parts?

1200cm3
1100cm3
1050cm3
2100cm3
CorrectIncorrect
Correct answer is: 1050cm3
Volume of hemisphere =Volumeofsphere2=1050cm3
5

What is the volume of a sphere with a radius of 18 cm?

8004.78cm3
9304.88cm3
3908.78cm3
3052.08cm3
CorrectIncorrect
Correct answer is: 3052.08cm3
Diameter of the sphere =18cm
Radius of the sphere =182=9cm
The volume of the sphere = V =43πr3=43×3.14×9×9×9=3052.08cm3

Frequently Asked Questions

The relation between the volume of a sphere and a cylinder is that the volume of the sphere is two-thirds of the magnitude of the cylinder with a height equal to the sphere’s diameter and the same radius.

The general formula for the volume of a sphere is given as V =43πr3 . Let’s say “d” is its diameter. According to the definition of diameter, we have d =2r. From this, we get the value of radius =d2. Substituting this in the formula, the volume of a sphere can be found.

For a sphere, the surface area is S = 4*π*R*R, where R is the sphere’s radius, and π is 3.1415… The volume of a sphere is V =4×R×R×R3. So for a sphere, the surface area to volume ratio is given by: SV=3R.

The volume of a sphere is measured in cubic units, such as m3,cm3, etc.

Balls, balloons, globes, marbles, and lollipops are some real-life examples of a sphere.