Question

The radius of the sphere is expressed as (5.3±0.1) cm. Find the percentage error in the volume of the sphere

Answer 1

V = (4/3)πr3

so,

V = (4/3) x 3.14 x 5.33

thus,

V = 623.30 cm3

now, the error equation

ΔV/V = 3(Δr/r)

or

ΔV = V x 3(Δr/r)

thus,

ΔV = 623.30 x 3x(0.1/5.3)

or error in surface area

ΔV = +/- 35.28 cm3

thus,

ΔV/V x 100 = (35.28/623.30) x 100

so,

ΔV/V x 100 = 5.66 %