Quantitative Ability - Volume and Surface Area (Important Formulas)

CUBOID

Let length = l, breath = b and height= h units. Then

i. Volume =(lxbxh) cubic units.

ii. Surface area =2(lb+bh+ih) sq.units.

iii. Diagonal = 1² + b² + h² units.

CUBE

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

iv. Volume = a³ cubic units.

V. Surface area = 6a² sq. units.

vi. Diagonal = 3a units.

CYLINDER

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

vii. Volume = (πr²h) cubic units.

viii. Curved surface area = (2πrh) sq. unit.

ix. Total surface area = 2πr (h+r) sq. unit.

CONE

Let radius of base = r and height = h. Then,

X. Slant height, l = h² + r² units.

Xi. Volume = (1/3 πr²h) cubic units

xii. Curved surface area = (πrl) sq. units.

xiii. Total surface area = (πrl + πr²) sq. units.

SPHERE

Let the radius of the sphere be r. Then,

xiv. Volume = (4/3 πr³) cubic units

xv. Surface area = (4π r²) sq. units.

HEMISPHERE

Let the radius of a hemisphere be r. Then,

xvi. Volume = (2/3 πr³) cubic Units.

xvii. Curved Surface area = (2πr²) sq. units.

xviii. Total Surface area = (3πr²) sq. units.

Note: 1 liter = 1000cm³.

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