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.

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

How to Calculate and Solve for the Area, Radius, Diameter and Slant Height of a Cone | The Calculator Encyclopedia

The image above is a cone.

To compute the area of a cone, two essential parameters is needed and this parameters are the radius of the cone (r) and the slant height of the cone (h).

The formula for calculating the area of a cone:

A = πrl + πr²

Where;

A = Area of the Cone
r = Radius of the Cone

Let’s solve an example:
Find the area of a cone when the radius of the cone is 9 cm and the slant height of the cone is 12 cm.

This implies that;
r = Radius of the cone = 9 cm
l = Slant height of the cone = 12 cm

A = πrl + πr²
A = 3.142 x 9 x 12 + 3.142 x 9²
A = 339.336 + 254.502
A =  593.83

Therefore, the area of the cone is 593.83 cm².

Calculating the Area of a cone using Diameter and Slant height of the cone.

A = πdl / 2 + πd2 / 4

Where;

d = Diameter of the Cone
l = Slant height of the Cone

Let’s solve an example:
Find the area of a cone when the diameter of the cone is 18 cm and the slant height of the cone is 22 cm?

This implies that;
d = diameter of the cone = 18 cm
l = Slant height of the cone = 22 cm

A = πdl / 2 + πd2 / 4
A = 3.142 x 18 x 22 / 2 + 3.142 (18)2 / 4
A = 1244.232 / 2 + 1018.008 / 4
A = 622.116 + 254.502
A = 876.6

Therefore, the area of the cone with diameter is 876.6 cm2.

Calculating the Slant height of a cone using Radius of the cone and Area of the cone.

l = A – πr2 / πr

Where;

A = Area of the Cone
r = Radius of the Cone

Let’s solve an example:
Find the slant height of a cone when the radius of the cone is 8 cm and the area of the cone is 220 cm2.

This implies that;
A = Area of the cone = 220 cm2
r = Radius of the cone = 8 cm

l = A – πr2 / πr
l = 220 – 3.142 x 82 / 3.142 x 8
l = 220 – 3.142 x 64 / 25.136
l = 220 – 201.088 / 25.136
l = 18.91 / 25.136
l = 0.75

Therefore, the slant height of the cone with radius is 0.75 cm.

Continue reading How to Calculate and Solve for the Area, Radius, Diameter and Slant Height of a Cone | The Calculator Encyclopedia

How to Calculate and Solve for the Perimeter or Circumference, Diameter, Radius and Angle of a Sector | The Calculator Encyclopedia

The image above is a sector.

To compute the Perimeter or Circumference a sector, two essential parameters is needed and this parameters are the radius of the sector (r) and the angle of the sector (θ). You can also use the diameter of the sector (d).

The formula for calculating the Perimeter or Circumference of a sector:

P = 2r + θ / 360(2πr)

Where;

P = Perimeter or Circumference
r = Radius of the sector
θ = Angle of the Sector

Let’s solve an example:
Find the perimeter or circumference of a sector when the radius of the sector is 14 cm and the angle of the sector is 60°

This implies that;

r = Radius of the sector = 14 cm
θ = Angle of the sector = 60°

P = 2r + θ / 360(2πr)
P = 2 x 14 + 60 / 360(2 x 3.142 x 14)
P = 28 + 0.1667 (87.97)
P = 28 + 14.66
P = 42.66

Therefore, the perimeter or circumference of the sector is 42.66 cm.

Calculating the Perimeter or Circumference of a Sector using Diameter and Angle of the sector.

P = d + θ / 360(πd)

θ = Angle of the sector
d = Diameter of the sector

Let’s solve an example;
Find the perimeter or circumference of a sector when the diameter of the sector is 20 cm and the angle of the sector is 80°.

This implies that;

d = Diameter of the sector = 20 cm
θ = Angle of the sector = 80°

Continue reading How to Calculate and Solve for the Perimeter or Circumference, Diameter, Radius and Angle of a Sector | The Calculator Encyclopedia

How to Calculate and Solve for the Area, Radius, Diameter and Angle of a Sector | The Calculator Encyclopedia

The image above is a sector.

To compute the area of a sector, two essential parameters is needed and this parameters are the radius of the sector (r) and the angle of the sector (θ). You can also use the diameter of the sector (d).

The formula for calculating the area of a sector:

Area of a sector = (θ/360)[πr²]

Where;

A = Area of the Sector
r = Radius of the Sector
θ = Angle of the Sector

Let’s solve an example:
Find the area of a sector when the radius of the sector is 7 cm and the angle of the sector is 9°

This implies that;

r = Radius of the sector = 7 cm
θ = Angle of the sector = 9°

A = θ / 360 x πr2
A = (9/360)[π x 7²]
A = 0.025 x π x 49
A = 3.848

Therefore, the area of the sector is 3.848 cm2.

Calculating the Area of a Sector using Diameter and Angle of the sector.

The formula is A = θ / 360 x πd2 / 4

Where;

θ = Angle of the sector
d = Diameter of the sector

Let’s solve an example;
Find the Area of a sector when the diameter of the sector is 12 cm and the angle of the sector is 18°.

This implies that;

d = Diameter of the sector = 12 cm
θ = Angle of the sector = 18°

A = θ / 360 x πd2 / 4
A = 18 / 360 x 3.142 (144) / 4
A = 18 / 360 x 452.448 / 4
A= 18 / 360 x 113.112
A= 0.05 x 113.112
A = 5.656

Therefore, the area of the sector with diameter is 5.656 cm

How to Calculate Angle of a Sector when Area of the Sector and Radius of the Sector is Given

θ = 360 (A) / πr2

where;

r = Radius of a sector
A = Area of a sector

Let’s solve an example;
Given that the area of a sector is 15 cm2 and the radius of the sector is 5 cm. Find the angle of the sector?

This implies that;
A = Area of the sector = 15 cm2
r = Radius of the sector = 5 cm

θ = 360 (A) / πr2
θ = 360 (15) / 3.142 (5)2
θ = 5400 / 3.142 (25)
θ = 5400 / 78.55
θ = 68.746

Therefore, the angle of the sector is 68.746°.

How to Calculate Angle of a Sector when Area of the Sector and Diameter of the Sector is Given

θ = 1440 (A) / πd2

where;

d = Diameter of a sector
A = Area of a sector

Let’s solve an example;
Given that the area of a sector is 22 cm2 and the diameter of the sector is 10 cm. Find the angle of the sector?

This implies that;
A = Area of the sector = 22 cm2
d = Diameter of the sector = 10 cm

θ = 1440 (A) / πr2
θ = 1440 (22) / 3.142 (10)2
θ = 31680 / 3.142 (100)
θ = 31680 / 314.2
θ = 100.88

Therefore, the angle of the sector is 100.88°.

How to Calculate Diameter of a Sector when Area of the Sector and Angle of the Sector is Given

d = √1440 (A) / πθ

where;

θ = Angle of a sector
A = Area of a sector

Let’s solve an example;
Given that the area of a sector is 24 cm2 and the angle of the sector is 10°. Find the diameter of the sector?

This implies that;
A = Area of the sector = 24 cm2
θ = Angle of the sector = 10°

d = √1440 (A) / πθ
d = √1440 (24) / 3.142 x 10
d = √34560 / 31.42
d = √1099.936
d = 33.165

Therefore, the diameter of the sector is 33.165 cm.

How to Calculate Radius of a Sector when Area of the Sector and Angle of the Sector is Given

r = √360 (A) / πθ

where;

θ = Angle of a sector
A = Area of a sector

Continue reading How to Calculate and Solve for the Area, Radius, Diameter and Angle of a Sector | The Calculator Encyclopedia

How to Calculate and Solve for the Volume, Radius and Height of a Cylinder | Nickzom Calculator

The image above represents a cylinder.
To compute the volume of a cylinder requires two essential parameters which are the radius and height of the cylinder.

The formula for computing the volume of a cylinder is:

V = πr2h

Where:
V = Volume of a cylinder
r = radius of the cylinder
h = height of the cylinder

Let’s solve an example
Find the volume of a cylinder with a radius of 3 cm and a height of 5 cm.

This implies that:
r = radius of the cylinder = 3
h = height of the cylinder = 5

V = πr2h
V = 3.142 x 32 x 5
V = 141.39

Therefore, the volume of the cylinder is 141.39 cm3.

Calculating the Height of a cylinder when Volume and Radius is Given

The formula is h = V / πr2

Where;
V = Volume of a cylinder
r =  radius of the cylinder
h = height of the cylinder

Let’s solve an example:
Find the height of a cylinder with a volume of 300 cm3 and a radius of 3 cm

This implies that;
V = Volume of the cylinder = 300 cm3
r  = radius of the cylinder = 3 cm

h = V / πr2
h = 300 / 3.142(3)2
h = 300 / 28.278
h = 10.61
Therefore, the height of the cylinder is 10.61 cm.

Calculating the Radius of a cylinder when Volume and Height is Given

The formula is r = √(V / πh)

Where;
V = Volume of a cylinder
r =  radius of the cylinder
h = height of the cylinder

Let’s solve an example:
Find the radius of a cylinder with a volume of 200 cm3 and a height of 5 cm

This implies that;
V = Volume of the cylinder = 200 cm3
h  = height of the cylinder = 5 cm

r = √(V / πh)
r = √(200 / 3.142(5))
r = √(200 / 15.71)
r = √12.73
r = 3.57

Therefore, the radius of the cylinder is 3.57 cm.

Continue reading How to Calculate and Solve for the Volume, Radius and Height of a Cylinder | Nickzom Calculator

How to Calculate the Area, Radius and Height of a Cylinder | Nickzom Calculator

The image above represents a cylinder.
To compute the area of a cylinder requires two essential parameters which are the radius and height of the cylinder.

The formula for computing the area of a cylinder is:

A = 2πrh + 2πr2

Where:
A = Area of a cylinder
r = radius of the cylinder
h = height of the cylinder

Let’s solve an example
Find the area of a cylinder with a radius of 3 cm and a height of 5 cm.

This implies that:
r = radius of the cylinder = 3
h = height of the cylinder = 5

A = 2πrh + 2πr2
A = 2(3.142) x 3 x 5 + 2(3.142) x 32
A = 150.82

Therefore, the area of the cylinder is 150.82 cm2.

Calculating the Height of a cylinder when Area and Radius is Given

The formula is h =  A/ 2πr – r

Where;
A = Area of a cylinder
r =  radius of the cylinder
h = height of the cylinder

Let’s solve an example:
Find the height of a cylinder with an area of 600 cm² and a radius of 5 cm

This implies that;
A = Area of the cylinder = 600 cm²
r  = radius of the cylinder = 5 cm

h = A / 2πr – r
h = 600 / 2(3.142)(5) – 5
h = 600 / 31.42 – 5
h = 19.10 – 5
h = 14.10

Therefore, the height of the cylinder is 14.10 cm.

Continue reading How to Calculate the Area, Radius and Height of a Cylinder | Nickzom Calculator

How to Calculate and Solve for the Perimeter or Circumference, Radius and Diameter of a Circle | The Calculator Encyclopedia

The image above is a circle.

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

The formula for calculating the perimeter or circumference of a circle is:

P = 2πr

Where:

P = Perimeter or Circumference of a circle
r = Radius of a circle

Let’s solve an example:
Find the perimeter or circumference of a circle where the radius of a circle is 8 cm.

This implies that;
r = Radius of a circle = 8 cm

P = 2πr
P = 2 x 3.142 x 8
P = 50.265

Therefore, the perimeter or circumference of a circle is 50.265 cm.

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

The formula is P = πd

Where:

P = Perimeter or Circumference of a circle
d = Diameter of a circle

Let’s solve an example:
Find the perimeter or circumference of a circle where the diameter of a circle is 10 cm.

This implies that;
d = Diameter of a circle = 10 cm

P = πd
P = 3.142 x 10
P = 31.42

Therefore, the perimeter or circumference of a circle with diameter is 31.42 cm.

How to Calculate Radius of a Circle when Perimeter or Circumference of the Circle is Given

r = P /

where;

r = Radius of a circle
P = Perimeter or Circumference of a circle

Let’s solve an example:
Find the radius of a circle where the perimeter or circumference of the circle is 16 cm.

This implies that;
P = Perimeter or Circumference of the circle = 16 cm

r = P /
r = 16 / 6.284
r = 2.55

Therefore, the radius of the circle is 2.55 cm.

How to Calculate Diameter of a Circle when Perimeter or Circumference of the Circle is Given

d = P / π

where;

d = Diameter of a circle
P = Perimeter or Circumference of a circle

Let’s solve an example;
Find the diameter of a circle where the perimeter or circumference of the circle is 20 cm

This implies that;
P = Perimeter or Circumference of the circle = 20 cm

d = P / π
d = 20 / π
d = 6.365

Therefore, the diameter of the circle is 6.365 cm.

Continue reading How to Calculate and Solve for the Perimeter or Circumference, Radius and Diameter of a Circle | The Calculator Encyclopedia

How To Calculate and Solve for the Area, Radius and Diameter of a Circle | The Calculator Encyclopedia

The image above is a circle.

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

The formula for calculating the area of a circle is:

A = πr2

Where:

A = Area of a circle
r = Radius of a circle

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

This implies that;
r = Radius of a circle = 6 cm

A = πr2
A = 3.142 (6)2
A = 3.142 (36)
A = 113.10

Therefore, the area of a circle is 113.10 cm2

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

The formula is A = πd2/4

Where;
A = Area of a circle
d = Diameter of a circle

Let’s solve an example:
Find the area of a circle where the diameter of the circle is 7 cm.

This implies that;
d = Diameter of a circle = 4 cm

A = πd2 / 4
A = 3.142 (4)2 / 4
A = 3.142 (16) / 4
A = 3.142 (4)
A = 12.57

Therefore, the area of a circle with diameter given is 12.57 cm2

Continue reading How To Calculate and Solve for the Area, Radius and Diameter of a Circle | The Calculator Encyclopedia

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.

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

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

The image above is a hemisphere with a radius of 5.
To compute the centroid or centre of gravity of a hemisphere. You need one essential parameter and this parameter is the radius of the hemisphere (r).

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

C.G. = 3r / 8

Where
r = Radius of the hemisphere

As always let us try and solve an example:
Find the centroid or centre of gravity of a hemisphere where the radius is 5 cm.

From the formula this implies that:
r = Radius of the hemisphere = 5

C.G. = 3(5) / 8
C.G. = 15 / 8
C.G. = 1.875

Therefore, the centroid or centre of gravity of the hemisphere is 1.875.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a hemisphere at a distance from its base measured along the vertical radius.

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

You can get this app via any of these means:

Continue reading How to Calculate and Solve for the Centroid or Centre of Gravity of a Hemisphere