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)3 × 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 ft3 = 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
