Question

If the error in the measurement of radius is 2%, then the error in the determination of volume of the spere will be a) 8%, b) 2% c) 4% d) 6%
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Answer 1

Answer:

$2 + 2 = 4$

Hope it will help for you

Answer 2

Answer:

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