Question

A sphere ohas a radius of5cm measured to an accuracy of 0.1 cm. Find the percentage error in the measurement of its volume.

Answer 1

Dear Student,
The volume is given as

V = (4/3)πr³

so,

V = (4/3) x 3.14 x 5³

thus,

V = 523.33 cm³

Now, the error equation,

ΔV/V = 3(Δr/r)

or

ΔV = V x 3(Δr/r)

thus,

ΔV = 523.33 x 3x(0.1/5)

ΔV = +/- 31.39cm³

thus,

ΔV/V x 100 =31.39/523.33 X 100

so,

ΔV/V x 100 = 5.99 %