Question

If the error in the measurement of radius is 2%, then the error in the determination of volume of the sphere will be
a) 8%
c) 4%
b) 2%
d) 6%

Answer 1

Volume of sphere , V= 4/3 πr³
now, differentiate both sides,
so, dV = 4πr²dr
Now, divide by V both sides,
dV/V = 4πr²dr/V
⇒dV/V = 4πr²dr/{4/3πr³}
⇒ dV/V = 3dr/r

Hence, for finding error in volume of sphere,
Use the formula, % error in Volume = 3 × % error in radius
given, % error in radius = 2 %
∴ % error in volume = 3 × 2 = 6 %

Hence, option ( d) is correct

Answer 2

Answer:6%

Explanation:volume of sphere =4/3πr^3

∆v/v=3∆r/r %

=3×2%

6%