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(C) Volume of a sphere is given by $V_s = \frac{4}{3} \pi r^3$.Volume of a right circular cylinder is given by $V_c = \pi r^2 h$.Given that the volume

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(C) Volume of a sphere is given by $V_s = \frac{4}{3} \pi r^3$.Volume of a right circular cylinder is given by $V_c = \pi r^2 h$.Given that the volumes are equal,we have $\frac{4}{3} \pi r^3 = \pi r^2 h$.Simplifying this,we get $h = \frac{4}{3} r$.The diameter of the cylinder is $d = 2r$.The difference between the diameter and the height is $d - h = 2r - \frac{4}{3} r = \frac{2}{3} r$.The percentage by which the diameter exceeds the height is $\frac{d - h}{h} 	imes 100 = \frac{\frac{2}{3} r}{\frac{4}{3} r} 	imes 100 = \frac{2}{4} 	imes 100 = 50 \%$.

$A$ sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

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