Question

The volume V of a cylinder of height h and radius r is given by the expression V = π  r2h. In a particular experiment, r is to be determined from measurements of V and h. The percentage uncertainty in V is ±5% and that in h is ±2%. Calculate the percentage uncertainty in r.

Answer 1

Answer:

Uncertainty in r = 3.5 %

Explanation:

Volume of a cylinder = πr²h [area of crossection x height]

rearrange for r and you get

r² = V/(πh)

r = √(V/πh)

The rule of dealing with uncertainties in mathematical calculations;

• you add percentage uncertainties when you multiply or divide quantities.

• if a quantity is squared you double the uncertainty, if cubed it is 3 times etc. i.e. multiply by the index. Square root is index half so divide by 2.

Uncertainty in r will be (5% + 2%)/2

Uncertainty in r = 3.5 %