Source: Extra Practice
If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of its volume will be:
Options
Option A is correct
6%
Option B
2%
Option C
4%
Option D
8%
Explanation
Volume of a sphere V = (4/3)πr³. The relative error is ΔV/V = 3(Δr/r). Given Δr/r = 2%, the percentage error in volume is 3 × 2% = 6%. 2% is the error in radius, 4% would be the error in surface area (r²), and 8% is a calculation error.