Question

2. A sphere has a radius of 5.00 cm. with an uncertainty of 5%,

a) what is the percent uncertainty of the volume? _______%

b) What is the volume of sphere with absolute uncertainty? _____ +/ _____cm^3

Answer 1

The percent uncertainty of the volume=
`(15.70)/(523.59) * 100=2.99\%`

The volume of sphere with absolute uncertainty=
`523.59 \pm 15.7 cm^3`

Step-by-step explanation:

Radius of sphere = 5 cm

Radius with uncertainty r'=
`5 \pm 0.05`

Volume of sphere =
`(4)/(3) \pi r^3=(4)/(3) \pi (r')^3`

`V=(4)/(3) \pi (r')^3\\(dV)/(dr')=4\pi (r')^2`

Where dV is the uncertainty in volume

dr' is the uncertainty in radius

`dV=4\pi (r')^2 dr'\\dV=4 \pi (5)^2(0.05)\\dV=15.70\\V=(4)/(3) \pi (r')^3=(4)/(3) \pi (5)^3=523.59`

The percent uncertainty of the volume=
`(15.70)/(523.59) * 100=2.99\%`

The volume of sphere with absolute uncertainty=
`523.59 \pm 15.7 cm^3`