How to Calculate and Solve for True Stress | The Calculator Encyclopedia

The image above represents the true stress.

To compute for the true stress, two essential parameters are needed and these parameters are force (F) and instantaneous area (Ai).

The formula for calculating true stress:

σT = F / Ai

Where;
T = True Stress
F = Force
Ai = Instantaneous Area

Let’s solve an example;
Find the true stress when the instantaneous area is 60 with a force of 25.

This implies that;
F = Force = 25
Ai = Instantaneous Area = 60

σT = F / Ai
σT = 25 / 60
σT = 0.416

Therefore, the true stress is 0.416 Pa.

Calculating the Force when True Stress and Instantaneous Area is Given.

F = Ai x σT

Where;
F = Force
σT = True Stress
Ai = Instantaneous Area

Let’s solve an example;
Find the force when the instantaneous area is 30 with a true stress of 15.

This implies that;
σT = True Stress = 15
Ai = Instantaneous Area = 30

F = Ai x σT
F = 30 x 15
F = 450

Therefore, the force is 450.

Continue reading How to Calculate and Solve for True Stress | The Calculator Encyclopedia

How to Calculate and Solve for the Height, Base Edge and Area of a Square Pyramid | Nickzom Calculator

The image above is a square pyramid.

To compute the area of a square pyramid, two essential parameters are needed and this parameters are base edge (a) and height (h).

The formula for calculating the area of a square pyramid:

A = a² + 2a√(( / 4) + h²)

Where;
A = Area of a square pyramid
a = Base edge of the square pyramid
h = Height of the square pyramid

Let’s solve for an example;
Find the area of a square pyramid when the base edge (a) given is 8 cm with a height (h) of 12 cm.

This implies that;
a = Base edge of the square pyramid = 8 cm
h = Height of the square pyramid = 12 cm

A = a² + 2a√(( / 4) + h²)
A = 8² + 2 x 8√(( / 4) + 12²)
A = 64 + 16√((64 / 4) + 144)
A = 64 + 16√(16 + 144)
A = 64 + (16)(√160)
A = 64 + (16)(12.65)
A = 64 + 202.3857
A = 266.386

Therefore, the area of the square pyramid is 266.386 cm2.

Continue reading How to Calculate and Solve for the Height, Base Edge and Area of a Square Pyramid | Nickzom Calculator

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