The volumes of a right circular cylinder and | vedclass

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(D) Let the radius of the cylinder be $r$ and its height be $h$.Let the radius of the sphere be $R$.Given that the radius of the cylinder is equal to

Vedclass · Accepted Answer

$1:6$

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(D) Let the radius of the cylinder be $r$ and its height be $h$.Let the radius of the sphere be $R$.Given that the radius of the cylinder is equal to the diameter of the sphere,we have $r = 2R$,which implies $R = r/2$.The volume of the cylinder is $V_c = \pi r^2 h$.The volume of the sphere is $V_s = \frac{4}{3} \pi R^3$.Since the volumes are equal,$\pi r^2 h = \frac{4}{3} \pi R^3$.Substituting $R = r/2$ into the equation:$\pi r^2 h = \frac{4}{3} \pi (r/2)^3$$\pi r^2 h = \frac{4}{3} \pi (r^3 / 8)$$r^2 h = \frac{4}{24} r^3$$r^2 h = \frac{1}{6} r^3$Dividing both sides by $r^2$ (assuming $r 
eq 0$):$h = \frac{1}{6} r$Therefore,the ratio of the height to the radius of the cylinder is $h/r = 1/6$.

The volumes of a right circular cylinder and a sphere are equal. The radius of the cylinder and the diameter of the sphere are equal. The ratio of the height to the radius of the cylinder is:

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