## How to Calculate and Solve for the Radius, Height and Surface Area of a Spherical Segment | The Calculator Encyclopedia

The image above is a spherical segment.

To compute the surface area of a spherical segment requires two essential parameters which are the radius of the sphere (R) and the height (h).

The formula for calculating the surface area of the spherical segment:

A = 2πRh

Where;
A = Surface area of the spherical segment
R = Radius of the sphere
h = Height of the spherical segment

Let’s solve an example;
Find the surface area of a spherical segment when the radius of the sphere is 12 cm and the height is 16 cm.

This implies that;
R = Radius of the sphere = 12 cm
h = Height of the spherical segment = 16 cm

A = 2πRh
A = 2π (12 x 16)
A = 2π (192)
A = 6.28 (192)
A = 1206.37

Therefore, the surface area of the spherical segment is 1206.37 cm2.

Calculating the Radius of the Sphere using the Surface Area of the Spherical Segment and the Height.

R = A / 2πh

Where;
R = Radius of the sphere
A = Surface area of the spherical segment
h = Height of the spherical segment

Let’s solve an example;
Find the radius of a sphere with a surface area of 300 cm2 and a height of 12 cm.

This implies that;
A = Surface area of the spherical segment = 300 cm2
h = Height of the spherical segment = 12 cm

R = A / 2πh
R = 300 / 2 x π x 12
R = 300 / 75.41
R = 3.978

Therefore, the radius of the sphere is 3.978 cm.

## How to Calculate and Solve for the Volume of a Spherical Segment | Nickzom Calculator

The image above is a spherical segment.

To compute the volume of a spherical segment requires three essential parameters which are the radius of the spherical segment base (r1), radius of the spherical segment (r2) and height (h).

The formula for calculating the volume of the spherical segment:

V = πh(3r1² + 3r2² + h²)6

Where;
V = Volume of the spherical cap
r1 = Radius of the spherical segment base
r2 = Radius of the spherical segment base
h = Height of the spherical segment

Let’s solve an example;
Find the volume of a spherical segment when the radius of the spherical segment base (r1) is 7 cm, radius of the spherical segment base (r2) is 9 cm and a height of 20 cm.

This implies that;
r1 = Radius of the spherical segment base = 7 cm
r2 = Radius of the spherical segment base = 9 cm
h = Height of the spherical segment = 20 cm

V = πh(3r1² + 3r2² + h²)6
V = π x 20(3 x 7² + 3 x 9² + 20²)6
V = π x 20(3 x 49 + 3 x 81 + 400)6
V = π x 20(147 + 243 + 400)6
V = π x 20(790)6
V = π x 158006
V = 49643.66
V = 8273.9

Therefore, the volume of the spherical segment is 8273.9 cm3.

## How to Calculate the Radius, Height and Curved Surface Area of a Spherical Cap | The Calculator Encyclopedia

The image above is a spherical cap.

To compute the curved surface area of a spherical cap requires two essential parameters which are the radius of the base of the cap (a) and the height (h).

The formula for calculating the curved surface area of the spherical cap:

A = π(a² + h²)

Where;
A = Curved surface area of the spherical cap
a = Radius of the base of the cap
h = Height of the spherical cap

Let’s solve an example;
Find the curved surface area of a spherical cap with radius of the base 7 cm and the height of 13 cm.

This implies that;
a = Radius of the base of the cap = 7 cm
h = Height of the spherical cap = 13 cm

A = π(a² + h²)
A =  π(7² + 13²)
A =  π(49 + 169)
A =  π(218)
A = 684.867

Therefore, the curved surface area of the spherical cap is 684.867 cm².

Calculating the Radius of the base of a Spherical Cap using the Curved Surface Area of the Spherical Cap and the Height.

a = √A – πh2 / π

Where;
A = Curved surface area of the spherical cap
a = Radius of the base of the cap
h = Height of the spherical cap

Let’s solve an example;
Find the radius of the base of a spherical cap when the curved surface area of the spherical cap is 300 cm2 and a height of 7 cm.

This implies that;
A = Curved surface area of the spherical cap = 300 cm2
h = Height of the spherical cap = 7 cm

a = √A – πh2 / π
a = √300 – 3.142 x 72 / π
a = √300 – 3.142 x 49 / π
a = √300 – 153.958 / π
a = √146.042 / π
a = √46.48
a = 6.82

Therefore, the radius of the base of the cap is 6.82 cm.

## How to Calculate and Solve for the Volume of a Spherical Cap | Nickzom Calculator

The image above is a spherical cap.

To compute the volume of a spherical cap requires two essential parameters which are the radius of the base of the cap (a) and the height (h).

The formula for calculating the volume of the spherical cap:

V = πh(3a² + h²) ⁄ 6

Where;
V = Volume of the spherical cap
a = Radius of the base of the cap
h = Height of the spherical cap

Lets solve an example;
Find the volume of a spherical cap when the radius of the base is 12 cm and the height is 22 cm.

This implies that;
a = Radius of the base of the cap = 12 cm
h = Height of the spherical cap = 22 cm

V = πh(3a² + h²) ⁄ 6
V = 3.142 (22)(3(12)² + 22²) ⁄ 6
V = 3.142 (22)(3(144) + 484) ⁄ 6
V = 3.142 (22)(432 + 484) ⁄ 6
V = 3.142 (22)(916) ⁄ 6
V = 3.142 (20152)6
V = 63309.37 ⁄ 6
V = 10551.56

Therefore, the volume of the spherical cap is 10551.56 cm2.

## How to Calculate and Solve for the Total Surface Area of a Conical Frustum | The Calculator Encyclopedia

The image above is a conical frustum.

To compute the total surface area of a conical frustum requires three essential parameters which are the radius of the lower base (R), radius of the upper base (r) and the height (h).

The formula for calculating the total surface area of a conical frustum;

A = π[R² + r² + (R + r)√((R – r)² + h²)]

Where;
A = Total surface area of the conical frustum
R = Radius of the lower base
r = Radius of the upper base
h = Height of the conical frustum

Let’s solve an example;
Find the total surface area of the conical frustum when the radius of the upper base is 11 cm, radius of the lower base is 17 cm and the height is 30 cm.

This implies that;
r = Radius of the upper base = 11 cm
R = Radius of the lower base = 17 cm
h = Height of the conical frustum = 30 cm

A = π[R² + r² + (R + r)√((R – r)² + h²)]
A = π[17² + 11² + (17 + 11)√((17 – 11)² + 30²)]
A = π[289 + 121 + (28)√((6)² + 900)]
A = π[289 + 121 + (28)√(36+ 900)]
A = π[289 + 121 + (28)√(936)]
A = π[289 + 121 + (28)(30.59)]
A = π[289 + 121 + 856.63]
A = π[1266.63]
A = 3979.25

Therefore, the total surface area of the conical frustum is 3979.25 cm².

## How to Calculate and Solve for the Lateral Surface Area of a Conical Frustum | Nickzom Calculator

The image above is a conical frustum.

To compute the lateral surface area of a conical frustum requires three essential parameters which are the radius of the lower base (R), radius of the upper base (r) and the height (h).

The formula for calculating the lateral surface area of a conical frustum:

A = π(R + r)√((R – r)² + h²)

Where;
A = Area of the conical frustum
R = Radius of the lower base
r = Radius of the upper base
h = Height of the conical frustum

Let’s solve an example;
Given that the height of a conical frustum is 28 cm with a radius of lower base of 22 cm and a radius of upper base of 19 cm. Find the lateral surface area of the conical frustum?

This implies that;
h = Height of the conical frustum = 28 cm
R = Radius of the lower base = 22 cm
r = Radius of the upper base = 19 cm

A = π(R + r)√((R – r)² + h²)
A = 3.142(22 + 19)√((22 – 19)² + 28²)
A = 3.142(41)√((3)² + 28²)
A = 3.142 (41)√(9 + 784)
A = 3.142 (41)√(793)
A = 3.142 (41)(28.16)
A = 3.142 x 1154.56
A = 3627.63

Therefore, the lateral surface area of the conical frustum is 3627.63 cm².

## 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.

## How to Calculate and Solve for the Width, Height, Length and Volume of a Rectangular Prism | Nickzom Calculator

The image above is a rectangular prism.

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

V = lwh

Where;
V = Volume 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 volume of a rectangular prism with a length of 18 cm, a width of 12 cm and a height of 21 cm.

This implies that;
l = Length of the rectangular prism = 18 cm
w = Width of the rectangular prism = 12 cm
h = Height of the rectangular prism = 21 cm

V = lwh
V = 18 x 12 x 21
V = 4536

Therefore, the volume of the rectangular prism is 4536 cm3.

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

l = V / wh

Where;
l = Length of the rectangular prism
V = Volume 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 19 cm, a height of 24 cm and a Volume of 250 cm3.

This implies that;
w = Width of the rectangular prism = 19 cm
h = Height of the rectangular prism = 24 cm
V = Volume of the rectangular prism = 250 cm3

l = V / wh
l = 250 / 19 x 24
l = 250 / 456
l = 0.55

Therefore, the length of the rectangular prism is 0.55 cm.

## How to Calculate and Solve for the Height, Base Edge and Volume of a Square Pyramid | The Calculator Encyclopedia

The image above represents a square pyramid.
To compute the volume of a square pyramid requires two essential parameters which are the base edge and height of the square pyramid.

The formula for computing the volume of a square pyramid is:

V = ha² / 3

Where:
V = Volume of the Square Pyramid
a = Base edge of the Square Pyramid
h = Height of the Square Pyramid

Let’s solve an example
Find the volume of a square pyramid with a base edge of 6 cm and a height of 11 cm.

This implies that:
a = base edge of the square pyramid = 6
h= = height of the square pyramid = 11

V = ha² / 3
V = 11(6)² / 3
V = 11(36) / 3
V = 396 / 3
V = 132

Therefore, the volume of the square pyramid is 132 cm3.

Calculating the Base edge of a square pyramid when Volume and Height are Given

The formula is a = √(3V / h)

Where;
V = Volume of the Square Pyramid
a = Base edge of the Square Pyramid
h = Height of the Square Pyramid

Let’s solve an example:
Find the base edge of a square pyramid with a volume of 50 cm3 and a height of 20 cm.

This implies that;
V = Volume of the square pyramid = 50 cm3
h  = height of the square pyramid = 20 cm

a = √(3V / h)
a = √(3(50) / 20)
a = √(150 / 20)
a = √7.5
a = 2.739

Therefore, the base edge of the square pyramid is 2.739 cm.

Calculating the height of a square pyramid when Volume and Base edge are Given

The formula is h = 3V / a2

Where;
a = Base edge of the square pyramid
V = Volume of the Square Pyramid
h = Height of the Square Pyramid

Let’s solve an example:
Find the height of a square pyramid with a volume of  250 cm3  and a base edge of 7 cm2

This implies that;
V = Volume of the square pyramid = 250 cm3
a = Base edge of the square pyramid = 7 cm

h =  3V /
h = 3(250) /
h = 750 / 49
h = 15.306

Therefore, the height of the square pyramid is 15.306 cm.

## How to Calculate the Volume, Base Area and Height of a Prism | The Calculator Encyclopedia

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

The formula for computing the volume of a prism is:

V = Ah

Where:
V = Volume of the Prism
A = Base area of the Prism
h = Height of the prism

Let’s solve an example
Find the volume of a prism with a base area of 30 cm2 and a height of 8 cm.

This implies that:
A = base area of the prism = 30
h= = height of the prism = 8

V = Ah
V = 30 x 8
V = 240

Therefore, the volume of the prism is 240 cm3.

Calculating the Base area of a prism when Volume and Height are Given

The formula is A = V / h

Where;
V = Volume of the Prism
A = Base area of the Prism
h = Height of the Prism

Let’s solve an example:
Find the base area of a prism with a volume of 300 cm3 and a height of 12 cm.

This implies that;
V = Volume of the prism = 300 cm3
h  = height of the prism = 12 cm

A =  V / h
A = 300 / 12
A = 25

Therefore, the base area of the prism is 25 cm2.

Calculating the height of a prism when Volume and Base area are Given

The formula is h = V / A

Where;
A = Base area of the Prism
V = Volume of the Prism
h = Height of the Prism

Let’s solve an example:
Find the height of a prism with a volume of  280 cm3  and a base area of 35 cm2

This implies that;
V = Volume of the prism = 280 cm3
A = Base area of the prism = 35 cm2

h =  V / A
h = 280 / 35
h = 8

Therefore, the height of the prism is 8 cm.