If the radius of a sphere is measured as 7 te | vedclass

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Question

(D) Given, radius $(r) = 7 	ext{ m}$ and error in radius $(dr) = 0.02 	ext{ m}$.The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Differe

Vedclass · Accepted Answer

$3.92$

Vedclass · Answer

(D) Given, radius $(r) = 7 	ext{ m}$ and error in radius $(dr) = 0.02 	ext{ m}$.The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Differentiating with respect to $r$, we get $\frac{dV}{dr} = 4 \pi r^2$.The approximate error in volume $(dV)$ is given by $dV = \frac{dV}{dr} 	imes dr$.Substituting the values, $dV = 4 \pi (7)^2 	imes 0.02$.$dV = 4 \pi (49) 	imes 0.02$.$dV = 196 \pi 	imes 0.02 = 3.92 \pi 	ext{ m}^3$.Thus, the approximate error in calculating the volume is $3.92 \pi 	ext{ m}^3$. Therefore, option $(D)$ is correct.

If the radius of a sphere is measured as $7 \text{ m}$ with an error of $0.02 \text{ m}$, then the approximate error in calculating its volume is (in $\pi \text{ m}^3$)

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