Question

a spherical ball is measured to have a radius of 6 c mwith a possible measurement error of plus-or-minus 0.1 rm c m. use the differentials to estimate the percentage error in computing the volume of the ball.

Answer 1

Percentage error in computing volume is 10%;

r = 6 cm;

Possible measurement error , dr = ±0.1;

dr = 0.1-(0.1) = 0.2 cm;

Volume, V = 4/3 πr³ -(1)

Differentiate w.r.t. r;

dV/dr = 4πr²;  -(2)

Divide (2) by (1);

dV/V = 3 (dr/r)

Put value of r = 6 cm, dr = 0.2 cm;

dV/V = 0.1

Percentage error in computing volume = dV/V × 100% = 10%;

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