Volume of Sphere
The volume of a sphere is the measurement of the space it can occupy. Sphere is a threedimensional shape which has no edges or vertices. In this short lesson, we will learn to find the volume of a sphere, deduce the formula of volume of a sphere and learn to apply the formulas as well. Once you understand this chapter you will learn to solve problems on the volume of the sphere.
1.  What is the Volume of Sphere? 
2.  Derivation of Volume of Sphere 
3.  Formula of Volume of Sphere 
4.  How to Calculate the Volume of Sphere? 
5.  FAQs on Volume of Sphere 
What is the Volume of Sphere?
Volume of a sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.
The unit of volume of a sphere is given as the (unit)^{3}. The metric units of volume are cubic meters or cubic centimeters while the USCS units of volume are, cubic inches or cubic feet. The volume of sphere depends on the radius of the sphere, hence changing it changes the volume of the sphere. There are two types of spheres, solid sphere, and hollow sphere. The volume of both types of spheres is different. We will learn in the following sections about their volumes.
Derivation of Volume of Sphere
As suggested by Archimedes, if the radius of the cylinder, cone, and the sphere is "r" and they have the same crosssectional area, their volumes are in the ratio of 1:2:3. Hence, the relation between volume of sphere, volume of cone and volume of cylinder is given as:
Volume of Cylinder = Volume of Cone + Volume of Sphere
⇒ Volume of Sphere = Volume of Cylinder  Volume of Cone
As we know, volume of cylinder = πr^{2}h and volume of cone = onethird of volume of cylinder = (1/3)πr^{2}h
Volume of Sphere = Volume of Cylinder  Volume of Cone
⇒ Volume of Sphere = πr^{2}h  (1/3)πr^{2}h = (2/3)πr^{2}h
In this case, height of cylinder = diameter of sphere = 2r
Hence, volume of sphere is (2/3)πr^{2}h = (2/3)πr^{2}(2r) = (4/3)πr^{3}
Formula of Volume of Sphere
The formula of volume of sphere can be given for a solid as well as hollow sphere. In the case of a solid sphere, we only have one radius but in the case of a hollow sphere, there are two radii, having two different values of radius one for the outer sphere and one for the inner sphere.
Volume of Solid Sphere
If the radius of the sphere formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = (4/3)πr^{3}
Volume of Hollow Sphere
If the radius of the outer sphere is R, the radius of the inner sphere is r and the volume of the sphere is V. Then, the volume of the sphere is given by:
Volume of Sphere, V = Volume of Outer Sphere  Volume of Inner Sphere = (4/3)πR^{3}  (4/3)πr^{3} = (4/3)π(R^{3 } r^{3})
How to Calculate Volume of Sphere?
The volume of sphere is the space occupied inside a sphere. The volume of the sphere can be calculated using the formula of volume of a sphere. The steps to calculate the volume of a sphere are:
 Step 1: Check the value of radius of the sphere.
 Step 2: Take the cube of the radius by multiplying it by itself.
 Step 3: Multiply r^{3} by (4/3)π
 Step 4: At last, add the units to the final answer.
Let us take an example to learn how to calculate the volume of a sphere using its formula.
Example: Find the volume of sphere having radius of 4 inches.
Solution: As we know, the volume of sphere, V = (4/3)πr^{3}
Here, r = 4 inches
Thus, volume of sphere, V = (4/3)πr^{3} = ((4/3) × π × 4^{3}) in^{3}
⇒ V = 268.08 in^{3}
∴ The volume of sphere is 268.08 in^{3}.
Solved Examples on Volume of Sphere

Example 1: What is the amount of air that can be held by a spherical ball of diameter 14 inches?
Solution: We need to find the volume of the ball.
The radius of the ball will be half the diameter = 14/2 inches = 7 inchesThe volume of the ball is
Volume of the ball = (4/3)πr^{3 }= ((4/3) × (22/7) × 7^{3}) =1436.75 in^{3}
∴ The amount of air that can be held by the spherical ball of diameter 14 inches is 1436.75 cubic inches. 
Example 2: Maria has three wax marbles of radii 6 inches, 8 inches, and 10 inches. She melted all the marbles to recast them into a single solid marble. Can you find the radius of the resulting marble?
Solution: Let the radius of 3 marbles be \(r_{1}\), \(r_{2}\) and \(r_{3}\) and the radius of resulting marble is R.
Volume of resulting marble = Volume of marble 1 + Volume of marble 2 + Volume of marble 3
(4/3)πR^{3 }= (4/3)π\((r_{1})\)^{3 }+(4/3)π\((r_{2})\)^{3} + (4/3)π\((r_{3})\)^{3}
⇒ R^{3 }= ( \((r_{1}\))^{3}+ (\(r_{2}\))^{3}+ (\(r_{3}\))^{3 }
⇒ R^{3} = 6^{3} + 8^{3} + 10^{3} = 1728
⇒ R = 12 inches∴ The radius of the resulting marble is 12 inches.
FAQs on Volume of Sphere
What is the Volume of a Sphere?
The volume of a sphere is the amount of air that a sphere can be held inside it. The formula for calculating the volume of a sphere with radius 'r' is given by the formula volume of sphere = (4/3)πr^{3}.
How to Calculate the Volume of a Sphere?
We can calculate the volume of a sphere using the belowgiven steps:
 Step 1: First find the value of radius or diameter.
 Step 2: Use the formula of volume of sphere (4/3)πr^{3}.
 Step 3: Write the unit in the end, once the value is obtained.
What are the Three Dimensions of a Sphere?
Just like a circle, a sphere also has a radius and a diameter. A radius is only the dimension we need to calculate the volume of a sphere.
What is the Relation Between the Volume of Sphere and the Volume of Cylinder?
The relation between the volume of the sphere and the volume of the cylinder is that the volume of the sphere is twothird of the volume of the cylinder with a height equal to the diameter of the sphere and the same radius.
What is the Ratio of the Surface Area to the Volume of the Sphere of Unit Radius?
The formula of volume of a sphere = (4/3)πr^{3} and formula of the surface area of sphere = 4πr^{2}. Hence, the ratio of surface area to the volume of the sphere of unit radius is ((4/3/)π)/4π = 1:3
How Does the Volume of Sphere Change When the Radius of Sphere is Halved?
The volume of sphere gets one eighth when the radius is halved as r = r/2. As, volume of sphere = (4/3)πr^{3} = (4/3)π(r/2)^{3} = (4/3)πr^{3}/8 = volume/8. Thus, volume of sphere gets one eighth as soon as its radius gets halved.