Question

The radius of a sphere is determined to be 3.3 +/- 0.10 cm. What is the uncertainty in the volume of the sphere in cm^3?

Answer 1

Answer:

The volume is given as

V=(4/3)πr

3

so, V= (4/3)×3.14×5.33

thus,

V = 623.30cm

3

Now, the error equation

ΔV/V=3(Δr/r)

ΔV=V×3(Δr/r)

thus,

ΔV=623.30×3×(0.1/5.3)

ΔV=35.28cm

3

thus,

ΔV/V×100=(35.28/623.30)×100

so,

ΔV/V×100=5.66%