A right cylinder and a right circular cone ha | vedclass

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(D) Let the radius of both the cylinder and the cone be $r$.Let the height of the cylinder be $h$ and the height of the cone be $H$.The volume of a cy

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$1:3$

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(D) Let the radius of both the cylinder and the cone be $r$.Let the height of the cylinder be $h$ and the height of the cone be $H$.The volume of a cylinder is given by $V_{cylinder} = \pi r^{2} h$.The volume of a right circular cone is given by $V_{cone} = \frac{1}{3} \pi r^{2} H$.According to the problem,the volumes are equal,so:$\pi r^{2} h = \frac{1}{3} \pi r^{2} H$Dividing both sides by $\pi r^{2}$,we get:$h = \frac{1}{3} H$Therefore,the ratio of the height of the cylinder to the height of the cone is:$\frac{h}{H} = \frac{1}{3} = 1:3$.

$A$ right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is

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