How to Calculate and Solve for Mass, Volume and Density | The Calculator Encyclopedia

The image above represents density.

To compute for the density, two essential parameters are needed and these parameters are mass (m) and volume (v).

The formula for calculating density:

Density = mass / volume

Let’s solve an example;
Given that the volume is 20 m³ with a mass of 240 kg. Find the density?

This implies that;
Volume = 20
Mass = 240

Density = mass / volume
Density = 240 / 20
Density = 12

Therefore, the density is 12 Kg/m³.

Calculating the Mass when the Density and Volume is Given.

Mass = Volume x Density

Let’s solve an example;
With a density of 90 kg/m³ and a volume of 15 m³, Find the mass?

This implies that;
Density = 90
Volume = 15

Mass = Volume x Density
Mass = 15 x 90
Mass = 1350

Therefore, the mass is 1350 kg.

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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 Centre of Gravity of a Cube

The image above is a cube with a length of 5.2 cm.
To compute the centre of gravity of a cube, one essential parameter is needed and this parameter is the length of the cube (l).

The formula for calculating the centre of gravity of a cube is:

C.G. = 0.5(l)

Where:
l = Length of the Cube
C.G. = Centre of Gravity

Let’s solve an example:
Find the centre of gravity of a cube where the length of a side of the cube is 5.2 cm.

This implies that:
l = Length of the Cube = 5.2

Continue reading How to Calculate and Solve for the Centre of Gravity of a Cube

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:

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Nickzom Calculator Calculates the Centroid or Centre of Gravity of a Semicircle | Statics (Mechanics)

The image above is a semicircle with a radius of 7 cm.
To compute the centroid or centre of gravity of a semicircle, you need one essential parameter and this parameter is the radius of the semicircle.

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

C.G.= 4r /

Where:
r = Radius of the Semicircle
π = Mathematical Constant = 3.142 (approximately)

Let’s solve an example:
Find the centroid or centre of gravity of a semicircle where the radius is 7 cm.

From the example above,
r = radius of the semicircle = 7

C.G. = 4(7) /
C.G. = 28 / 9.4247
C.G. = 2.97

Therefore, the centroid or centre of gravity of the semicircle is 2.97.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a semicircle 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 semicircle using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

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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:

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

How to Calculate and Solve the Centre of Gravity of a Right Circular Cone

This image above is a display of what a right circular cone looks like. There is only one essential parameter for calculating the centroid or centre of gravity of a right circular cone. This parameter is the height of the cone (h).

The formula for calculating the the centroid or centre of gravity of a right circular cone is:

C.G. = h / 4

As always let’s solve an example.

Find the centroid or centre of gravity of a right circular cone where the height of the cone is 12cm.
This implies that:

h = height of the cone = 12

C.G. = 12 / 4
C.G. = 3

Therefore, the centroid or centre of gravity of the right circular cone is 3.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a right circular cone at a distance from its base measured along the vertical axis.

To get the answer and workings to center of gravity or centroid of a right circular cone 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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How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

It is very possible to compute the centroid or centre of gravity of a circular sector. There are two highly important parameters one needs to know to compute the centre of gravity of a circular sector. These parameters are:

  • Radius of the Sector (r)
  • Semi Vertical Angle (α)

The formula for computing the centre of gravity of a circular sector is:

C.G. = 2rsinα /

Now, let’s take an example.
Let’s find the centroid or the centre of gravity of a circular sector that has a radius of 4m and a semi vertical angle of 30°.
This implies that:

r = Radius of the Sector = 4
α = Semi Vertical Angle = 30

Entering this values into the formula we have:

C.G. = 2(4)sin30° / 3(30)
C.G. = 8 . sin30° / 90
C.G. = 8 . (0.5) / 90
C.G. = 4 / 90
C.G. = 0.0444

Therefore, the centroid or centre of gravity of the circular sector is 0.0444.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a circular sector making a semi vertical angle α at a distance from the centre of the sector measured along the central axis.

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

Continue reading How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

Nickzom Calculator Calculates the Center of Gravity of a Trapezium in Statics Mechanics

According to Quora,

The center of gravity of a trapezoid can be estimated by dividing the trapezoid in two triangles.

Nickzom Calculator calculates the centre of gravity of a trapezium with parallel sides a and b at a distance measured from side b.

The formula for calculating this center of gravity is:

C.G. = h (b + 2a) / 3 (b + a)

Where, a and b are the length of the parallel sides of the trapezium (b being the base length and a being the top length) whereas h is the height of the trapezium.

Let’s take for Example: Find the center of gravity or centroid of a trapezium where a is 4, b is 8 and h is 2.

This implies:

a = 4
b = 8
h = 2

C.G. = 2 (8 + 2(4)) / 3 (8 + 4)
C.G. = 2 (8 + 8) / 3 (12)
C.G. = 2 (16) / 36
C.G. = 32 / 36
C.G. = 0.89

Therefore, the center of gravity or centroid of the trapezium is 0.89.

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

Continue reading Nickzom Calculator Calculates the Center of Gravity of a Trapezium in Statics Mechanics

The Calculator Encyclopedia Calculates the Hydraulic Mean Depth or Hydraulic Radius of Flow in Open Channels | Fluid Mechanics

Hydraulic mean depth or hydraulic radius can be defined as the cross-sectional area of flow divided by wetted perimeter.

Wetted perimeter is the perimeter of the cross sectional area that is “wet”.
Hydraulic mean depth or hydraulic radius is a very important parameter in flow in open channels and fluid mechanics calculations.

The formula for computing hydraulic mean depth or hydraulic radius is:

R = A / P

Where:
R = Hydraulic Depth
A = Cross-sectional Area of Flow
P =  Wetted Perimeter

For Example:

Find the hydraulic mean depth or hydraulic radius of flow in an open channel where the cross-sectional area is 150 m2 and the wetted perimeter is 100 m.

From the example we can see that the cross-sectional area is 150 m2 and the wetted perimeter is 100 m.

R = 150 / 100
R = 1.5

Therefore, the hydraulic mean depth or hydraulic radius is 1.5 m.

Now, I would love to show you how to use Nickzom Calculator The Calculator Encyclopedia to get answers for your questions on hydraulic mean depth or hydraulic radius.

Continue reading The Calculator Encyclopedia Calculates the Hydraulic Mean Depth or Hydraulic Radius of Flow in Open Channels | Fluid Mechanics