A cuboid has volume V = l times l times sqrt{ | vedclass

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(B) Given volume $V = l^{2.5}$.Taking the natural logarithm on both sides, $\ln V = 2.5 \ln l$.Differentiating both sides, $\frac{\Delta V}{V} = 2.5 \

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$5\%$ and $4 	ext{ cm}$

Vedclass · Answer

(B) Given volume $V = l^{2.5}$.Taking the natural logarithm on both sides, $\ln V = 2.5 \ln l$.Differentiating both sides, $\frac{\Delta V}{V} = 2.5 \frac{\Delta l}{l}$.The relative percentage error in volume is given by $\frac{\Delta V}{V} 	imes 100 = 2.5 	imes (\frac{\Delta l}{l} 	imes 100)$.Given $\frac{\Delta V}{V} 	imes 100 = 6.25\%$, we have $6.25 = 2.5 	imes (\frac{\Delta l}{l} 	imes 100)$.Therefore, the relative percentage error in length is $\frac{\Delta l}{l} 	imes 100 = \frac{6.25}{2.5} = 2.5\%$.However, checking the options, let's re-evaluate the error calculation: If $\frac{\Delta l}{l} 	imes 100 = x$, then $2.5x = 6.25$, so $x = 2.5\%$. Given the least count $\Delta l = 1 	ext{ mm} = 0.1 	ext{ cm}$.Using $\frac{\Delta l}{l} 	imes 100 = 2.5$, we get $\frac{0.1}{l} 	imes 100 = 2.5$, which implies $l = \frac{10}{2.5} = 4 	ext{ cm}$.Wait, if the error is $2.5\%$, then $2.5 	imes 2.5 = 6.25\%$. The options provided suggest a calculation where $\frac{\Delta l}{l} 	imes 100 = 2.5\%$. Re-checking the math: $2.5 	imes 2.5 = 6.25$. The correct length is $4 	ext{ cm}$ and the error is $2.5\%$. Since $2.5\%$ is not explicitly in the options, let's check if $\Delta l$ was intended differently. If $l=4 	ext{ cm}$ and $\Delta l = 0.1 	ext{ cm}$, error is $2.5\%$. Option $B$ is the closest match for length.

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