Here, we provide you with volume formulas for some common three-dimensional figures and also for the ellipsoid and the hollow cylinder that are not so common.

Volume = a

Volume = π × r

π = 3.14

h is the height

r is the radius

Volume = l × w × h

l is the length

w is the width

h is the height

Volume = (4 × π × r

π = 3.14

r is the radius

Volume = (π × r

pi = 3.14

r is the radius

h is the height

Volume = (B × h)/3

B is the area of the base

h is the height

Volume = (4 × π × a × b × c)/3

Use π = 3.14

Volume = π × R

Volume = π × h ( R

Use π = 3.14.

**Volume of a cube **

The length of a side = a = 2 cm

Volume = (2 cm) = 2 cm × 2 cm × 2 cm = 8 cm^{3} = 8 cubic centimeters

**Volume of a cylinder**

The height is 8 inches and the radius is 2 inches.

Volume = π × r^{2} × h = 3.14 × (2 in)^{2} × 8 in = 3.14 × 4 × 8 in^{3}Volume = 3.14 × 32 in^{3} = 100.48 in^{2} = 100.48 cubic inches

**Volume of a cuboid or rectangular solid **

The length is 6 cm, the width is 3 cm and the height is 5 cm.

Volume = l × w × h = 6 × 3 × 5 = 90 cm^{3} = 90 cubic centimeters

**Volume of a sphere **

The radius = r = 20

Volume = (4 × π × r^{3})/3 = [4 × 3.14 × (20)^{3}]/3 = 3.14 × (20)^{3 }× 4

Volume = 3.14 × 8000 × 4 = 3.14 × 32000 = 100480

**Volume of a cone **

The radius is equal to 3 and the height is equal to 4.

Volume = (π × r^{2} × h)/3 = [3.14 × (3)^{2}× 4]/3 = 3.14 × 9^{ }× 4

Volume = 3.14 × 36 = 113.04

**Volume of a pyramid**

A pyramid has a height of 6 feet. If the base of a pyramid is a square with a length of 2 feet, find the volume.

Volume = (B × h)/3

B = area of base = 2 ft × 2 ft = 4 ft^{2}Volume = (4 × 6)/3 ft^{3 }= 24/3 ft^{3} = 8 ft^{3} = 8 cubic feet

**Volume of an ellipsoid**

The radii of an ellipsoid are 1 cm, 2, cm, and 3 cm.

Volume = (4 × π × a × b × c)/3 = (4 × 3.14 × 1 × 2 × 3)/3

Volume = ( 3.14 × 4 × 6)/3 = ( 3.14 × 24)/3 = 81.64/3 = 25.12 cm^{3} = 25.12 cubic centimeters

**Volume of a hollow cylinder**

The outer radius is 8, the internal radius is 6, and the height is 10.

Volume = π × h ( R^{2} - r^{2}) = π × 10 ( 8^{2} - 6^{2}) = π × 10 ( 64 - 36)

Volume = π × 10(28) = π × 280 = 879.2

The volume of a prism is the product of the area of a base and the height of the prism.

V = Bh

**A triangular prism**

**1.** Find the volume of the triangular prism shown in the image above using the formula below.

V = Bh

The dimensions of the triangular base are 12 m and 20 m.

The height of the triangular prism is h = 10 m.

B = area of the triangular base = (20 times 12)/2 = 240/2 = 120 m^{2}

V = 120 times 10 = 1200

The volume of the triangular prism is 1200 cubic meters.

**A trapezoidal prism**

**2.** Find the volume of the trapezoidal prism shown in the image above using the formula below.

V = Bh

The base of the trapezoidal prism is a trapezoid with the following dimensions.

b_{1} = 12 ft, b_{2} = 8 ft, and height = 7 feet.

The height of the trapezoidal prism is the perpendicular distance or 20 ft

B = area of the base = [(b_{1} + b_{2})h]/2

B = [(12 + 8)7]/2

B = [(20)7]/2

B = 140/2

B = 70 square feet

V = 70 times 20 = 1400

The volume of the trapezoidal prism is 1400 cubic feet