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(D) The volume of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.Given,radius $r = 2.1 \, cm$ and height $h = 8.4 \, cm$.Volume of cone $=

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$2.1$

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(D) The volume of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.Given,radius $r = 2.1 \, cm$ and height $h = 8.4 \, cm$.Volume of cone $= \frac{1}{3} \pi (2.1)^2 	imes 8.4$.When the cone is melted and recast into a sphere,the volume remains constant.Let the radius of the sphere be $R$. The volume of a sphere is $V = \frac{4}{3} \pi R^3$.Equating the volumes: $\frac{4}{3} \pi R^3 = \frac{1}{3} \pi (2.1)^2 	imes 8.4$.Dividing both sides by $\frac{1}{3} \pi$: $4 R^3 = (2.1)^2 	imes 8.4$.$R^3 = \frac{(2.1)^2 	imes 8.4}{4} = (2.1)^2 	imes 2.1 = (2.1)^3$.Taking the cube root on both sides,$R = 2.1 \, cm$.Thus,the radius of the sphere is $2.1 \, cm$.

$A$ cone is $8.4 \, cm$ high and the radius of its base is $2.1 \, cm$. It is melted and recast into a sphere. The radius of the sphere is (in $cm$):

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