Formula for Volume of sphere | How to find the volume of a sphere

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volume of sphere

Formula volume of sphere: Formula for volume of a sphere helps in the calculation of volume of sphere.  Below is the formulaes of volume of sphere and examples to how to find the volume of a sphere.

Volume of Sphere

The volume of a sphere is the quantity of space it occupies. The sphere is a 3-Dimensional figure with three axes such as x-axis, y-axis, z-axis. Volume of sphere depends on diameter and radius of sphere. Radius of sphere is the distance between fixed point at its center and any point on the surface of the sphere. Examples of sphere are football, volleyball, baseball etc. Its measurements are in cubic units ( m3, cm3, ft3, in3 etc ). 

The Formula of Volume of Sphere

Volume of sphere formula (V) = 4/3 × πr3 cubic units.
π value in numeric is 22/7 which is equal to 3.14

r is the radius of sphere.

The Formula for Volume of Sphere using Diameter

volume of a sphere with a diameter (V) = 4/3 × π(D/2)3 cubic units.

D is the diameter of a sphere.
Diameter of the sphere (D) = 2 × r

How to Find the Volume of a Sphere Examples

Q.1: Calculate the volume of a sphere whose radius is 7 cm.

Solution: 

Given the radius of the sphere, r = 7 cm.
From above Formula for volume of sphere (V) = 4/3 × πr3 cubic units.
V = 4/3 × 22/7 × 73
V = 4/3 × 22 × 7 × 7
V = 1437.33 cm3.

Q.2: Calculate the volume of a sphere whose diameter is 12 cm.

Solution: 

Given the diameter of the sphere, D = 12 cm.
Radius of sphere = Diameter of sphere/2 = 12/2 = 6cm
From above Formula for volume of sphere (V) = 4/3 × πr3 cubic units.
V = 4/3 × 22/7 × 63
V = 4 × 3.14 × 2 × 6 × 6  Since, π = 22/7 = 3.14
V = 904.32 cm3.

Q.3: Calculate the radius of a sphere whose volume is  38808 cm3 .

Solution: 

Given the volume of the sphere, V = 38808 cm.
From the above Formula for volume of sphere (V) = 4/3 × πr3 cubic units.
38808 = 4/3 × 22/7 × r3
r3 = 38808 × 7/22 × 3/4
r3 = 441 × 7 × 3
r3 =  7 × 3 × 7 × 3 × 7 × 3
r = 7 × 3
r = 21 cm

Q.4: Calculate the diameter of a sphere whose volume is  77616 cm3 .

Solution: 

Given the volume of the sphere, V = 77616 cm3.
volume of sphere using diameter (V) = 4/3 × π(D/2)3 cubic units.
77616 = 4/3 × 22/7 × (D/2)3
(D/2)3 = 77616 × 7/22 × 3/4
(D/2)3 = 882 × 7 × 3
(D/2)3 =  2 × 7 × 3 × 7 × 3 × 7 × 3
D/8 = 2 × 7 × 3
D = 336 cm

 

 

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