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

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(A) Let $r$ be the radius of the sphere and $\Delta r$ be the error in measuring the radius.Given, $r = 7 	ext{ m}$ and $\Delta r = 0.02 	ext{ m}$.T

Vedclass · Accepted Answer

$3.92$

Vedclass · Answer

(A) Let $r$ be the radius of the sphere and $\Delta r$ be the error in measuring the radius.Given, $r = 7 	ext{ m}$ and $\Delta r = 0.02 	ext{ m}$.The volume $V$ 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 $\Delta V$ is given by $\Delta V \approx \frac{dV}{dr} \cdot \Delta r$.Substituting the values, $\Delta V \approx (4 \pi r^2) \cdot \Delta r$.$\Delta V \approx 4 \pi (7)^2 \cdot (0.02) = 4 \pi (49) (0.02) = 196 \pi (0.02) = 3.92 \pi 	ext{ m}^3$.Thus, the approximate error in calculating the volume is $3.92 \pi 	ext{ m}^3$.

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

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