In the measurement of volume of solid sphere using the formula V=4/3πr³ if the error committed in the measurement of the radius r is 1.5%, the percentage error in the volume measurement is

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1.5%

4.5%

0.75%

answer is C.

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Detailed Solution

Given the volume formula for a sphere: V = (4/3)πr³, the volume V is directly proportional to the cube of the radius r. Therefore, any percentage error in measuring the radius results in a percentage error in the volume that is three times greater.

If the error in measuring the radius r is 1.5%, the corresponding percentage error in the volume V is calculated as:

Percentage error in V = 3 × (Percentage error in r) = 3 × 1.5% = 4.5%

Thus, the percentage error in the volume measurement is 4.5%.

This aligns with the general principle that for measurements involving powers, the relative error in the calculated quantity is the exponent times the relative error in the measured quantity.

Correct Option:

c) 4.5%

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