How to Calculate and Solve for the Area of an Ellipsoid | The Calculator Encyclopedia

The image above is an ellipsoid.

To compute the area of an ellipsoid, three essential parameters are needed and this parameters are axis (a)axis (b) and axis (c).

The formula for calculating the area of an ellipsoid:

A = 4π((ab)1.6 + (ac)1.6 + (bc)1.63)1 / 1.6

Where;
A = Area of the ellipsoid
a = Axis of the ellipsoid
b = Axis of the ellipsoid
c = Axis of the ellipsoid

Let’s solve an example;
Find the the area of an ellipsoid when the axis (a) of the ellipsoid is 12 cm, axis (b) of the ellipsoid is 6 cm and axis (c) of the ellipsoid is 2 cm.

This implies that;
a = Axis of the ellipsoid = 12 cm
b = Axis of the ellipsoid = 6 cm
c = Axis of the ellipsoid = 2 cm

A = 4π((ab)1.6 + (ac)1.6 + (bc)1.63)1 / 1.6
A = 4π(((12)(6))1.6 + ((12)(2))1.6 + ((6)(2))1.63)1 / 1.6
A = 4π(((72)1.6 + (24)1.6 + (12)1.6)3)1 / 1.6
A = 4π(((936.98) + (161.56) + (53.29))3)1 / 1.6
A = 4π((1151.84)3)1 / 1.6
A = 4π(383.946)1 / 1.6
A = 4π(383.946)0.625
A = 4π(41.2258)
A = (12.566)(41.2258)
A = 518.059

Therefore, the area of the ellipsoid is 518.059 cm2.

Continue reading How to Calculate and Solve for the Area of an Ellipsoid | The Calculator Encyclopedia

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

The image above is a rectangular prism.

To compute the area of a rectangular prism requires three essential parameters which are the length, width and height of the rectangular prism.

A = 2wl + 2hl + 2hw

Where;
A = Area of the rectangular prism
l = Length of the rectangular prism
w = Width of the rectangular prism
h = Height of the rectangular prism

Let’s solve an example;
Find the area of a rectangular prism with a width of 10 cm, a height of 17 cm and a length of 14 cm.

This implies that;
l = Length of the rectangular prism = 14 cm
w = Width of the rectangular prism = 10 cm
h = Height of the rectangular prism = 17 cm

A = 2wl + 2hl + 2hw
A = 2 x 10 x 14 + 2 x 17 x 14 + 2 x 17 x 10
A = 280 + 476 + 340
A = 1096

Therefore, the area of the rectangular prism is 1096 cm2.

Calculating the Length of a Rectangular Prism using the Area, Width and Height of the Rectangular Prism. 

l = A – 2hw / 2 (w + h)

Where;
l = Length of the rectangular prism
A = Area of the rectangular prism
w = Width of the rectangular prism
h = Height of the rectangular prism

Let’s solve an example;
Find the length of a rectangular prism with a width of 9 cm, a height of 12 cm and a Area of 250 cm2.

This implies that;
w = Width of the rectangular prism = 9 cm
h = Height of the rectangular prism = 12 cm
A = Area of the rectangular prism = 250 cm2

l = A – 2hw / 2 (w + h)
l = 250 – 2 x 12 x 9 / 2 (9 + 12)
l = 250 – 216 / 2 (21)
l = 34 / 42
l = 0.81

Therefore, the length of the rectangular prism is 0.81 cm.

Continue reading How to Calculate and Solve for the Width, Height, Length and Area of a Rectangular Prism | The Calculator Encyclopedia

How to Calculate and Solve for the Axis and Area of an Ellipse | Nickzom Calculator

The image above is an ellipse.

To compute the area of an ellipse, two essential parameters are needed and this parameters are axis (a) and axis (b).

A = πab

Where;
A = Area of the ellipse
a = Axis of the ellipse
b = Axis of the ellipse

Let’s solve an example;
Find the area of an ellipse when it has an axis (a) of 10 cm and an axis (b) of 17 cm.

This implies that;
a = Axis of the ellipse = 10 cm
b = Axis of the ellipse = 17 cm

A = πab
A = 3.142 x 10 x 17
A = 534.14

Therefore, the area of the ellipse is 534.14 cm2.

Calculating the Axis (a) of an ellipse using Area of the ellipse and Axis (b) of the ellipse.

a = A / πb

Where;
a = Axis of the ellipse
A = Area of the ellipse
b = Axis of the ellipse

Let’s solve an example;
Find the axis (a) of an ellipse when the area of the ellipse is 210 cm2 with an axis (b) of 19 cm.

This implies that;
A = Area of the ellipse = 210 cm2
b = Axis of the ellipse = 19 cm

a = A / πb
a = 210 / 3.142 x 19
a = 210 / 59.70
a = 3.52

Therefore, the axis (a) of an ellipse is 3.52 cm.

Continue reading How to Calculate and Solve for the Axis and Area of an Ellipse | Nickzom Calculator

How to Calculate and Solve for the Length of a Side and Area of a Hexagon | The Calculator Encyclopedia

The image above is a hexagon.

To compute the area of a hexagon, one essential parameter is needed and this parameter is length of side (a).

The formula for calculating the area of a hexagon:

A = (a2)3√32

Where;
A = Area of the hexagon
a = Length of side

Let’s solve an example;
Find the area of a hexagon when the length of side is 35 cm.

A = (a2)3√32
A = (352)3√32
A = 1225 x 3(1.73)2
A = 1225 x 5.1962
A = 6365.2872
A = 3182.64

Therefore, the area of the hexagon is 3182.64 cm2.

Calculating the length of side (a) using the area of the hexagon.

a = √(2A3√3)

Where;
a = length of side
A = Area of the hexagon

Let’s solve an example;
Given that the area of the hexagon is 120 cm2. Find the length of side?

This implies that;
A = Area of the hexagon = 120 cm2

a = √(2A3√3)
a = √(2 x 1205.196)
a = √(2405.196)
a = √46.189
a = 6.796

Therefore, the length of side (a) is 6.796 cm.

Continue reading How to Calculate and Solve for the Length of a Side and Area of a Hexagon | The Calculator Encyclopedia

How to Calculate and Solve for the Length and Area of a Pentagon | Nickzom Calculator

The image above is a pentagon.

To compute the area of a pentagon, one essential parameter is needed and this parameter is length of side (a).

The formula for calculating the area of a pentagon:

A = a2(5(5 + 2√5) / 4

Where;
A = Area of the pentagon
a = length of side

Let’s solve an example;
Find the area of the pentagon when the length of side is 30 cm.

This implies that;
a = length of side = 30 cm

A = a2(5(5 + 2√5) / 4
A = 302(5(5 + 4.47) / 4
A = 900√(5(9.47) / 4
A = 900√47.36 / 4
A = 900√11.84
A = 900 x 3.44
A = 3096

Therefore, the area of the pentagon is 3096 cm2.

Calculating the length of side using the area of the pentagon.

a = √(4A / √5(5 + 2√5))

Where;
a = length of side
A = Area of the pentagon

Let’s solve an example;
Find the length of side with an area of 150 cm2.

This implies that;
A = Area of the pentagon = 150 cm2

a = √(4A / √5(5 + 2√5))
a = √(4 x 150 / √5(5 + 1.148))
a = √(600 / √5(6.148))
a = √(600 / √30.74)
a = √(600 / 5.54)
a = √108.30
a = 10.41

Therefore, the length of side is 10.41 cm.

Continue reading How to Calculate and Solve for the Length and Area of a Pentagon | Nickzom Calculator

How to Calculate and Solve for the Area, Length, Width and Height of a Cuboid | Nickzom Calculator

The image above represents a cuboid.
To compute the area of a cuboid requires three essential parameters which are the length, width and height of the cuboid.

The formula for computing the area of a cuboid is:

A = 2(lw + lh + wh)

Where:
A = Area of the Cuboid
l = Length of the Cuboid
w = Width of the Cuboid
h = Height of the Cuboid

Let’s solve an example
Find the area of a cuboid with a length of 5 cm, width of 3 cm and a height of 9 cm.

This implies that:
l = length of the cuboid = 5
w = width of the cuboid = 3
h= = height of the cuboid = 9

A = 2(lw + lh + wh)
A = 2(5 x 3 + 5 x 9 + 3 x 9)
A = 2(87)
A = 174

Therefore, the area of the cuboid is 174 cm2.

Calculating the Length of a cuboid when Area, Width and Height are Given

The formula is l = A – 2(w)(h) / 2(w) + 2(h)

Where;
A = Area of the Cuboid
l = Length of the Cuboid
w = Width of the Cuboid
h = Height of the Cuboid

Let’s solve an example:
Find the length of a cuboid with an area of 140 cm2 , a width of 4 cm and a height of 12 cm

This implies that;
A = Area of the cuboid = 140 cm2
w = width of the cuboid = 4 cm
h  = height of the cuboid = 12 cm

l =  A – 2(w)(h) / 2(w) + 2(h)
l = 140 – 2(4)(12) / 2(4) + 2(12)
l = 140 – 96 / 8 + 24
l = 44 / 32
l = 1.375 cm

Therefore, the length of the cuboid is 1.375 cm.

Calculating the Width of a cuboid when Area, Length and Height are Given

The formula is w = A – 2(l)(h) / 2(l) + 2(h)

Where;
A = Area of the Cuboid
l = Length of the Cuboid
w = Width of the Cuboid
h = Height of the Cuboid

Let’s solve an example:
Find the width of a cuboid with an area of 200 cm2 , a length of 5 cm and a height of 12 cm

This implies that;
A = Area of the cuboid = 200 cm2
l = length of the cuboid = 5 cm
h  = height of the cuboid = 12 cm

w =  A – 2(l)(h) / 2(l) + 2(h)
w = 200 – 2(5)(12) / 2(5) + 2(12)
w = 200 – 120 / 10 + 24
w = 80 / 34
w = 2.353 cm

Therefore, the width of the cuboid is 2.353 cm.

Calculating the Height of a cuboid when Area, Length and Width are Given

The formula is h = A – 2(l)(w) / 2(l) + 2(w)

Where;
A = Area of the Cuboid
l = Length of the Cuboid
w = Width of the Cuboid
h = Height of the Cuboid

Let’s solve an example:
Find the height of a cuboid with an area of 300 cm2 , a length of 6 cm and a width of 2 cm

This implies that;
A = Area of the cuboid = 300 cm2
l = length of the cuboid = 6 cm
w  = width of the cuboid = 2 cm

h =  A – 2(l)(w) / 2(l) + 2(w)
h = 300 – 2(6)(2) / 2(6) + 2(2)
h = 300 – 24 / 12 + 4
h = 276 / 16
h = 17.25 cm

Therefore, the height of the cuboid is 17.25 cm.

Continue reading How to Calculate and Solve for the Area, Length, Width and Height of a Cuboid | Nickzom Calculator

How to Calculate and Solve for the Length of the Diagonal and Area of a Rhombus | The Calculator Encyclopedia

The above image is a rhombus.

To compute the area of a rhombus, two essential parameters are needed and this parameters are length of the diagonal (p) and length of the diagonal (q).

The formula for calculating the area of a rhombus:

A = pq ⁄ 2

Where;
A = Area of the rhombus
p = length of the diagonal
q = length of the diagonal

Let’s solve an example;
Find the area of a rhombus when the length of the diagonal (p) is 10 cm and the length of the diagonal (q) is 18 cm.

This implies that;
p = length of the diagonal = 10 cm
q = length of the diagonal = 18 cm

A = pq2
A = 10 x 18 / 2
A = 180 / 2
A = 90

Therefore, the area of the rhombus is 90 cm2.

Calculating the length of the diagonal (p) using Area of the Rhombus and length of the diagonal (q).

p = 2A / q

Where;
A = Area of the rhombus
q = length of the diagonal

Let’s solve an example;
Given that the length of the diagonal (q) is 20 cm with an area of 60 cm2. Find the length of the diagonal (p)?

This implies that;
A = Area of the rhombus = 60 cm2
q = length of the diagonal = 20 cm


p = 2A / q
p = 2 x 60 / 20
p = 120 / 20
p = 6


Therefore, the length of the diagonal is 6 cm.

Continue reading How to Calculate and Solve for the Length of the Diagonal and Area of a Rhombus | 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 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