Topic 9: Measurement of Area & Volume

Measurement of Area

Area is the measure of the surface occupied by an object. It is derived from the measurement of length. The SI unit of area is square metre (m²).

Common Formulae for Area

Rectangle: Area = length × breadth
Square: Area = side²
Circle: Area = πr²
Triangle: Area = ½ × base × height

Measurement of Volume

Volume is the measure of the space occupied by a body. The SI unit of volume is cubic metre (m³).

Common Formulae for Volume

Cube: Volume = side³
Cuboid: Volume = length × breadth × height
Cylinder: Volume = πr²h
Sphere: Volume = 4/3 πr³

Error in Area and Volume Measurement

Since area and volume depend on length, any error in length measurement gets multiplied while calculating area and volume.

If percentage error in length is x%:

Percentage error in area = 2x%
Percentage error in volume = 3x%

Q1. SI unit of area is:
A) m
B) m²
C) m³
D) cm²
Answer: B

Q2. If percentage error in length is 2%, the percentage error in area is:
A) 2%
B) 4%
C) 6%
D) 8%
Answer: B

Q3. SI unit of volume is:
A) m²
B) cm³
C) litre
D) m³
Answer: D

Q4. Percentage error in volume is related to length error as:
A) Same
B) Double
C) Triple
D) Half
Answer: C

Q5. Which formula is correct for volume of a sphere?
A) πr²
B) 2πr
C) 4/3 πr³
D) πr³
Answer: C

Area & Volume – Quick Revision

Area

Derived quantity
SI unit: m²
Error in area = 2 × error in length

Volume

Derived quantity
SI unit: m³
Error in volume = 3 × error in length

Important Formulae

Rectangle: l × b
Circle: πr²
Cuboid: l × b × h
Sphere: 4/3 πr³

CET Exam Tip

Questions on percentage error in area and volume are very common. Remember: 2x for area, 3x for volume.

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