How to Calculate and Solve for the Volume and Radius of a Sphere | The Calculator Encyclopedia

The image above is a sphere.

To compute the volume of a sphere, one essential parameter is needed and this parameter is the radius of the sphere (r). You can also use diameter of the sphere (d).

The formula for calculating the volume of a sphere:

V = (4/3)πr³

Where;

V = Volume of the sphere
r = Radius of the sphere

Let’s solve an example:
Find the volume of a sphere when the radius of the sphere is 10 cm.

This implies that;

r = Radius of the sphere = 10 cm

V = (4/3)πr³
V = (4/3)π x (10)³
V = (4/3)π x 1000
V = (4/3)3.142 x 1000
V = (4/3)3142
V = 1.33 x 3142
V = 4188.7

Therefore, the volume of the sphere is 4188.7 cm³.

Calculating the Volume of a Sphere using Diameter of the Sphere.

V = 4πd³ / 24

Where;

V = Volume of the sphere
d = Diameter of the sphere

Let’s solve an example:
Find the volume of a sphere when the diameter of the sphere is 20 cm.

This implies that;

d = Diameter of the sphere = 20 cm

V = 4πd³ / 24
V = 4 x 3.142 x (20)³ / 24
V = 4 x 3.142 x 8000 / 24
V = 100544 / 24
V = 4189.3

Therefore, the volume of the sphere with diameter is 4189.3 cm3.

Calculating the Radius of a Sphere using Volume of the Sphere.

r = 3√(3V / )

Where;

V = Volume of the sphere
r = Radius of the sphere

Let’s solve an example:
Find the radius of a sphere when the volume of the sphere is 250 cm3.

This implies that;

V = Volume of the sphere = 250 cm3

r = 3√(3V / )
r = 3√(3 x 250 / 4 x 3.142)
r = 3√(750 / 12.568)
r = 3√59.675
r = 3.907

Therefore, the radius of the sphere is 3.907 cm.

Calculating the Diameter of a Sphere using Volume of the Sphere.

d = 3√(24V / )

Where;

A = Area of the sphere
d = Diameter of the sphere

Let’s solve an example:
Find the diameter of a sphere when the volume of the sphere is 40 cm3.

This implies that;

V = Volume of the sphere = 40 cm3

d = 3√(24V / )
d = 3√(24 x 40 / 4 x 3.142)
d = 3√(960 / 12.568)
d = 3√76.38
d = 4.24

Therefore, the diameter of the sphere is 4.24 cm.

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How to Calculate and Solve for the Area and Radius of a Sphere | Nickzom Calculator

The image above is a sphere.

To compute the area of a sphere, one essential parameter is needed and this parameter is the radius of the sphere (r). You can also use diameter of the sphere (d).

The formula for calculating the area of a sphere:

A = 4πr²

Where;

A = Area of the sphere
r = Radius of the sphere

Let’s solve an example:
Find the area of a sphere when the radius of the sphere is 6 cm.

This implies that;

r = Radius of the sphere = 6 cm

A = 4πr²
A = 4 x 3.142 x 6²
A = 4 x 3.142 x 36
A = 452.4

Therefore, the area of the sphere is 452.4 cm2.

Calculating the Area of a sphere using Diameter of the sphere.

A = πd2

Where;

A = Area of the sphere
d = Diameter of the sphere

Let’s solve an example:
Find the area of a sphere when the diameter of the sphere is 8 cm.

This implies that;

d = Diameter of the sphere = 8 cm

A = πd2
A = 3.142 x 82
A = 3.142 x 64
A = 201.08

Therefore, the area of the sphere is 201.08 cm2.

Calculating the Radius of a sphere using Area of the sphere.

r = √(A / )

Where;

A = Area of the sphere
r = Radius of the sphere

Let’s solve an example:
Find the radius of a sphere when the area of the sphere is 22 cm2.

This implies that;

A = Area of the sphere = 22 cm2

r = √(A / )
r = √(22 / 4 x 3.142)
r = √(22 / 12.57)
r = √1.75
r = 1.32

Therefore, the radius of the sphere is 1.32 cm.

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How to Calculate and Solve the Centre of Gravity of a Segment of a Sphere

The image above represents a segment of a sphere.
To compute the centre of gravity of a segment of a sphere requires two essential parameters. These parameters are the radius of the sphere and height of the segment of the sphere.

The formula for computing the centre of gravity of a sphere is:

C.G. = 3(2r – h)² / 4(3r – h)

Where:
C.G. = Centre of Gravity
r = Radius of the Sphere
h = Height of the Segment of the Sphere

Let’s solve an example
Find the centre of gravity of the segment of the sphere where the radius of the sphere is 10 m and the height of the segment of the sphere is 4 m.

This implies that:
r = Radius of the Sphere = 10
h = Height of the Segment of the Sphere = 4

C.G. = 3(2(10) – 4)² / 4(3(10) – 4)
C.G. = 3(20 – 4)² / 4(30 – 4)
C.G. = 3(16)² / 4(26)
C.G. = 3(256) / 104
C.G. = 768 / 104
C.G. = 7.38

Therefore, the centre of gravity of the segment of the sphere is 7.38.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a segment of a sphere at a height, h at a distance from the centre of the sphere measured along the height.

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How to Calculate and Solve for the Centroid or Centre of Gravity of a Sphere

The image above is a sphere and 18 m is the diameter of the sphere. In the computing of the centroid or centre of gravity of a sphere there is only one essential parameter which is the diameter of the sphere.

The formula for calculating the centroid or centre of gravity of a sphere is:

C.G. = d / 2

Where:

d is the diameter of the sphere

As always, let’s take an example:

Let’s solve an example
Find the centroid or centre of gravity of a sphere where the diameter is 18 m.

C.G. = 18 / 2
C.G. = 9

Therefore, the centroid or centre of gravity of the sphere is 9.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a sphere at a distance from every point.

To get the answer and workings of the center of gravity or centroid of a sphere using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

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