## 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.

## 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

## 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.

## How to Calculate and Solve for the Area and Length of a Parallelogram | The Calculator Encyclopedia

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

The formula for computing the area of a parallelogram is:

A = b x h

Where:
A = Area of a parallelogram
b = base of the parallelogram
h = height of the parallelogram

Let’s solve an example
Find the area of a parallelogram with a base of 12 cm and a height of 4 cm.

This implies that:
b = base of the parallelogram = 12
h = height of the parallelogram = 4

A = b x h
A = 12 x 4
A = 48

Therefore, the area of the parallelogram is 48 cm2.

Calculating the base of a parallelogram when Area and Height is Given

The formula is b = A / h

Where;
A = Area of a parallelogram
b = base of the parallelogram
h = height of the parallelogram

Let’s solve an example:
Find the base of a parallelogram with an area of 40 cm² and a height of 8 cm

This implies that;
A = Area of the parallelogram = 40 cm²
h = height of the parallelogram = 8 cm

b = A / h
b = 40 / 8
b = 5

Therefore, the base of the parallelogram is 5 cm.

Calculating the height of a parallelogram when Area and Base is Given

The formula is h = A / b

Where;
A = Area of a parallelogram
b = base of the parallelogram
h = height of the parallelogram

Let’s solve an example:
Find the height of a parallelogram with an area of 60 cm² and a base of 6 cm

This implies that;
A = Area of the parallelogram = 60 cm²
b = base of the parallelogram = 6 cm

h = A / b
h = 60 / 6
h = 10

Therefore, the height of the parallelogram is 10 cm.

## How to Calculate and Solve for the Area, Base and Height of a Triangle | The Calculator Encyclopedia

The image above is a triangle.
To compute the area of a triangle two essential parameters are required which are the base of the triangle and the height of the triangle.

The formula for calculating the area of a triangle is:

A = 0.5bh

Where:

A = Area of a Triangle
b = Base of a Triangle
h = Height of a Triangle

Let’s solve an example:
Given that the base of a triangle is 12 cm and the height of the triangle is 4 cm. Find the area of the triangle.

This implies that:
b = Base of the Triangle = 12 cm
h = Height of the Triangle = 4 cm

A = 0.5bh
A = 0.5(12)(4)
A = 0.5(48)
A = 24

Therefore, the area of the triangle is 24 cm2

How to Calculate the Base of a Triangle when the Area and Height of the Triangle is Given

The formula is:

b = 2A / h

Where:

b = Base of the Triangle
A = Area of the Triangle
h = Height of the Triangle

Let’s take an example:
Find the base of a triangle when the height and area of the triangle is 12 cm and 40 cm2 respectively.

This implies that:
A = Area of the Triangle = 40 cm2
h = Height of the Triangle = 12 cm

b = 2(40) / 12
b = 80 / 12
b = 6.667

Therefore, the base of the triangle is 6.667 cm.

How to Calculate the Height of a Triangle when the Area and Base of the Triangle is Given

The formula is:

h = 2A / b

Where:

## 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.

## How to Calculate and Solve for the Area, Width and Length of a Rectangle | The Calculator Encyclopedia

The image above is a rectangle with a length of 9 cm and a width of 4 cm.
To compute the area of a rectangle requires two essential parameters which are the length of the rectangle and the width of the rectangle.

The formula for calculating the area of a rectangle is:

A = lw

Where:

A = Area of a Rectangle
l = Length of a Rectangle
w = Width of a Rectangle

Let’s solve an example
Find the area of a rectangle where the length of the rectangle is 9 cm and the width of the rectangle is 4 cm.

This implies that:
l = Length of the Rectangle = 9 cm
w = Width of the Rectangle = 4 cm

A = lw
A = (9)(4)
A = 36

Therefore, the area of the rectangle is 36 cm2.

How to Calculate the Length of a Rectangle when the Area and Width of the Rectangle is Given

The formula for calculating the length of the rectangle is:

l = A / w

Where:

l = Length of the Rectangle
A = Area of the Rectangle
w = Width of the Rectangle

Let’s solve an example:
Find the length of a rectangle where the area of the rectangle is 45 cm2 and the width of the rectangle is 9 cm.

This implies that:
A = Area of the Rectangle = 45 cm2
w = Width of the Rectangle = 9 cm

l = A / w
l = 45 / 9
l = 5

Therefore, the length of the rectangle is 5 cm.

How to Calculate the Width of a Rectangle when the Area and Length of the Rectangle is Given

The formula for calculating the width of the rectangle is:

w = A / l

Where:

w = Width of the Rectangle
A = Area of the Rectangle
l = Length of the Rectangle

## How to Calculate and Solve for the Area and Length of a Square | The Calculator Encyclopedia

The image above represents a square.
To compute the area of a square requires one essential parameter which is the length of one side of a square.

The formula for computing the area of a square is:

A = l2

Where:
A = Area of a Square
l = Length of one side of a Square

Let’s solve an example
Find the area of a square which has a length of 6 ft.

This implies that:
l = length of one side of a square = 6

A = l2
A = 62
A = 6 x 6
A = 36

Therefore, the area of the square is 36 ft2.

Calculating the Length of a Square when Area is Given

The formula is l = √[A]

Where;
A = Area of a square
l = Length of a square

Let’s solve an example:
Find the length of a square where the area of a square is 81 ft2.

This implies that;
A = Area of a square = 81 ft2

l = √[A]
l = √[81]
l = 9

Therefore, the length of the square is 9 ft.

## 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

## How to Calculate and Solve for Linear Expansivity, Area Expansivity and Volume or Cubic Expansivity

Linear expansivity, area expansivity and volume or cubic expansivity are all parameters that are being governed by heat energy. All three parameter is dependent on temperature rise which is primarily in Celsius unit of temperature.

Linear expansivity additionally depends on the original length and final length, area expansivity additionally depends on the original area and final area and lastly, cubic or volume expansivity depends on the original volume and final volume.

The formula for calculating linear expansivity is (l2 – l1) / l1θ
l2 represents the final length.
l1 represents the original length.
θ represents the temperature rise in Celsius.

The formula for calculating area expansivity is (A2 – A1) / A1θ
A2 represents the final area.
A1 represents the original area.
θ represents the temperature rise in Celsius.

The formula for calculating volume or cubic expansivity is (V2 – V1) / V1θ
V2 represents the final volume.
V1 represents the original volume.
θ represents the temperature rise in Celsius.