Volume formulas

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.



Cube:

cube
Volume = a3 = a × a × a





Cylinder:

cylinder
Volume = π × r2 × h

π = 3.14
h is the height
r is the radius




Rectangular solid or cuboid:

Rectangular prism
Volume = l × w × h

l is the length
w is the width
h is the height




Sphere:

Sphere
Volume = (4 × π × r3)/3

π = 3.14
r is the radius




Cone:

Cone
Volume = (π × r2 × h)/3

pi = 3.14
r is the radius
h is the height



Pyramid:

Pyramid
Volume = (B × h)/3

B is the area of the base
h is the height

A little less common volume formulas



Ellipsoid:

Ellipsoid
Volume = (4 × π × a × b × c)/3

Use π = 3.14




Hollow cylinder:

Hollow cylinder
Volume = π × R2 × h - π × r2 × h

Volume = π × h ( R2 - r2)

Use π = 3.14.

How to use the volume formulas to calculate the volume.

Cube

The length of a side = a = 2 cm
Volume = (2 cm) = 2 cm × 2 cm × 2 cm = 8 cm3

Cylinder

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

Volume = π × r2 × h = 3.14 × (2 in)2 × 8 in = 3.14 × 4 × 8 in3
Volume = 3.14 × 32 in3 = 100.48 in3 

 Rectangular solid or cuboid 

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

Volume = l × w  × h =  6 × 3 × 5 = 90 cm3

Sphere 

The radius = r = 20 

Volume = (4 × π × r3)/3 = [4 × 3.14 × (20)3]/3 = 3.14 × (20)× 4
Volume = 3.14 × 8000 × 4 = 3.14 × 32000 = 100480

Cone 

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

Volume = (π × r2 × h)/3 = [3.14 × (3)2× 4]/3 = 3.14 × 9 × 4
Volume = 3.14 × 36 = 113.04

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 ft2
Volume = (4 × 6)/3 ft= 24/3 ft3 = 8 ft3

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 cm3 

Hollow cylinder

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

Volume = π × h ( R2 - r2) = π × 10 ( 82 - 62) = π × 10 ( 64 - 36)

Volume = π × 10(28) = π × 280 = 879.2

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