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The error in the measurement of the diam...

The error in the measurement of the diameter of a sphere is 2%. What is the percentage error in the measurement of its volume?

A

`4%`

B

`6%`

C

`8%`

D

`10%`

Text Solution

Verified by Experts

The correct Answer is:
b
`V=(4)/(3)pir^(3)=(4)/(3)pi((d)/(2))^(3)=(4)/(3)pi(d^(3))/(8)=(1)/(6)pid^(3)`
As `(1)/(6)` and `pi` are constants.
`therefore (deltaV)/(V)xx100=3((deltad)/(d))xx100=3xx2%=6%`
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