Aptitude - Volume Calculation

Important Fact and Formulae

Following are important facts and formulaes used in questions for volume calculations.

Cuboid

Let Length=L, Breath =b and Height =h units. Then,

• Volume = (L*b*h) cubic units.

• Surface area=2(Lb+bh+Lh) sq. units.

• Diagonal =√(L²+b²+h²) units.

Cube

Let each edge of a cube be of length a. Then,

• Volume=a³ cubic units.

• Surface area= 6a² sq. units.

• Diagonal= √3a units.

Cylinder

Let radius of base = r and Height (or length) =h. Then,

• Volume = (πr²h) cubic units.

• Curved surface area= (2πrh) sq. units.

• Total surface area= (2πrh+2πr²) sq. units. = 2πr (h+r) sq. units.

Cone

Let radius of base=r and Height (or length) = h. Then,

• Slant height=√h²+r² units.

• Volume = (1/3 πr²h) cubic units.

• Curved surface area = (πrL) sq. units.

• Total surface area = (πrL+ πr²) sq. units.

Sphere

Let the radius of the sphere be r. then,

• Volume = (4/3 πr³) cubic units.

• Surface area =( 4πr²) Sq. unit

Hemisphere

Let the radius of the hemisphere be r. then,

• (i) Volume = (2/3πr³) cubic units

• (ii) Curved surface area = (2πr²) Sq. unit

• (ii) Total surface area = 3πr² sq. unit.

Note:

1 litre = 1000cm³

Solved Examples