A solid metallic sphere of radius 10.5 , cm i | vedclass

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Question

(D) The volume of the solid metallic sphere is given by the formula $V_s = \frac{4}{3} \pi r^3$,where $r = 10.5 \, cm$.$V_s = \frac{4}{3} \pi (10.5)^3

Vedclass · Accepted Answer

$126$

Vedclass · Answer

(D) The volume of the solid metallic sphere is given by the formula $V_s = \frac{4}{3} \pi r^3$,where $r = 10.5 \, cm$.$V_s = \frac{4}{3} \pi (10.5)^3 \, cm^3$.The volume of one cone is given by the formula $V_c = \frac{1}{3} \pi r^2 h$,where $r = 3.5 \, cm$ and $h = 3 \, cm$.$V_c = \frac{1}{3} \pi (3.5)^2 	imes 3 \, cm^3 = \pi (3.5)^2 \, cm^3$.The number of cones formed is equal to the total volume of the sphere divided by the volume of one cone.$	ext{Number of cones} = \frac{V_s}{V_c} = \frac{\frac{4}{3} \pi (10.5)^3}{\pi (3.5)^2} = \frac{4 	imes 10.5 	imes 10.5 	imes 10.5}{3 	imes 3.5 	imes 3.5} = 4 	imes 3 	imes 3 	imes 3.5 = 126$.

$A$ solid metallic sphere of radius $10.5 \, cm$ is melted and recast into a number of smaller cones,each of radius $3.5 \, cm$ and height $3 \, cm$. Find the number of cones so formed.

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