Question

A uniform cylinder length and diameters are measured as 10+_0.1cm and 4+_0.2 mm respectively. Then absolute error in volume

Answer 1

Hey Dear,

◆ Answer -

Absolute error in volume = 0.1386 cm^3

● Explanation -

# Given -

l = 10 cm

∆l = 0.1 cm

d = 4 mm = 0.4 cm

∆d = 0.2 mm = 0.02 cm

# Solution -

Volume of the cylinder is given by -

V = A × l

V = π(d/2)^2 × l

V = π/4 d^2.l

V = 3.142/4 × 0.4^2 × 10

V = 1.26 cm^3

Thus, relative error in measurement of volume will be -

∆V/V = 2∆d/d + ∆l/l

∆V/V = 2 × 0.02 / 0.4 + 0.1/10

∆V/V = 0.1 + 0.01

∆V/V = 0.11

∆V = 0.11 × V

∆V = 0.11 × 1.26

∆V = 0.1386 cm^3

Hence, Absolute rror in measurement of volume is 0.1386 cm^3.

Thanks dear...