Question

Assume you measure the radius of a sphere with an uncertainty of 1%. What is the percentage of uncertainty in the volume? In the surface area? (Use approximation formulas).

Answer 1

If you measure the radius of a sphere with a 1% uncertainty, the percentage uncertainty in the volume and surface area can be approximated using the formulas:

Percentage uncertainty in volume = 3 times the percentage uncertainty in radius

Percentage uncertainty in surface area = 2 times the percentage uncertainty in radius

So, the percentage uncertainty in the volume would be approximately 3%, and the percentage uncertainty in the surface area would be approximately 2%.