How to Calculate and Solve for the Perimeter of a Trapezium | Nickzom Calculator

The image above is a trapezium.

To compute the perimeter of a trapezium, four essential parameters is needed and they are the length of the side (a), length of the side (b), length of the side (c) and length of the side (d).

The formula for calculating the perimeter of a trapezium is;

P = a + b + c + d

Where;

P = Perimeter of the trapezium
a = length of the side
b = length of the side
c = length of the side
d = length of the side

Let’s solve an example;
Find the perimeter of a trapezium with length of side (a) 4 cm, length of side (b) 8 cm, length of side (c) 12, length of side (d) 17 cm.

This implies that;
a = length of side = 4 cm
b = length of side = 8 cm
c = length of side = 12 cm
d = length of side = 17 cm

P = a + b + c + d
P = 4 + 8 + 12 + 17
P = 41

Therefore, the perimeter of the trapezium is 41 cm.

Continue reading How to Calculate and Solve for the Perimeter of a Trapezium | Nickzom Calculator

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.

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

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 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 Volume and Length of a Cube | The Calculator Encyclopedia

The image above is a cube.

To compute the volume of a cube, one essential parameter is needed and this parameter is the length of the cube (l).

The formula for calculating the volume of a cube is;

V = l3

Where;

V = Volume of a cube
l = Length of a cube

Let’s solve an example:
Find the volume of a cube where the length of a cube is 4 cm.

This implies that;
l = length of the cube = 4 cm.

V = l3
V = 43
V = 64 cm3

Therefore, the volume of the cube is 64 cm3

Calculating the Length of a cube using the Volume of the cube.

The formula is l = 3√V

Where;

V = Volume of a cube
l = length of a cube

Let’s solve an example:
Find the length of a cube where the volume of the cube is 120 cm3

This implies that;
V = Volume of the cube = 120 cm3

l = 3√V
l = 3√120
l = 4.93

Therefore, the length of the cube is 4.93 cm.

Continue reading How to Calculate and Solve for the Volume and Length of a Cube | The Calculator Encyclopedia

How to Calculate and Solve for the Area, Length and Height of a Trapezium | The Calculator Encyclopedia

The image above is a Trapezium

To compute the area of a trapezium, three essential parameter is needed and they are the length of the top side (a), length of the bottom side (b) and the height of the trapezium (h).

The formula for calculating the area of a trapezium is;

A = 0.5[a + b]h

Where;
A = Area of a trapezium
a = length of the top side of the trapezium
b = length of the bottom side of the trapezium
h = height of the trapezium

Let’s solve an example;
Find the area of a trapezium where length of top side (a) is 7 cm, length of bottom side (b) is 12 cm and height of trapezium (h) is 10 cm.

This implies that;
a = Length of top side of the trapezium = 7 cm
b = Length of bottom side of the trapezium = 12 cm
h = Height of the trapezium = 10 cm

A = 0.5[a + b]h
A = 0.5[7 + 12]10
A = 0.5[19]10
A = 95

Therefore, the area of a trapezium is 95 cm2

How to Calculate the Height of a Trapezium when the Area, Length of top side and Length of bottom side of the Trapezium is given.

The formula is h = A / 0.5(a + b)

Where;
A = Area of the trapezium
a = Length of the top side of the trapezium
b = Length of the bottom side of the trapezium

Let’s solve for an example;
Given that the length of top side (a) is 10 cm, length of bottom side (b) is 14 cm and the area of the trapezium is 20 cm2 Find the height of the trapezium?

This implies that;

A = Area of the trapezium = 20 cm2
a = Length of top side of the trapezium = 10 cm
b = Length of bottom side of the trapezium = 14 cm

h = A / 0.5(a + b)
h = 20 / 0.5(10 + 14)
h = 20 / 0.5(24)
h = 20 / 12
h = 1.667

Therefore, the height of the trapezium is 1.667 cm.

Continue reading How to Calculate and Solve for the Area, Length and Height of a Trapezium | 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