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(B) The volume of a cone is given by $V_{cone} = \frac{1}{3} \pi r^2 h_1$,where $r$ is the radius and $h_1$ is the height of the cone.The volume of a

Vedclass · Accepted Answer

$15$

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(B) The volume of a cone is given by $V_{cone} = \frac{1}{3} \pi r^2 h_1$,where $r$ is the radius and $h_1$ is the height of the cone.The volume of a cylinder is given by $V_{cylinder} = \pi r^2 h_2$,where $r$ is the radius and $h_2$ is the height of the cylinder.Since the material is converted from one shape to another,their volumes remain equal: $V_{cone} = V_{cylinder}$.$\frac{1}{3} \pi r^2 h_1 = \pi r^2 h_2$.Given that the radii are equal and the height of the cylinder $h_2 = 5\, cm$,we can cancel $\pi r^2$ from both sides:$\frac{1}{3} h_1 = 5$.$h_1 = 5 	imes 3 = 15\, cm$.Therefore,the height of the cone is $15\, cm$.

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is $5\, cm$,the height of the cone is........$cm$.

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