How many cones with diameter 7,cm and height | vedclass

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Question

(A) The volume of the metallic sphere with diameter $21\,cm$ (radius $R = 10.5\,cm$ or $21/2\,cm$) is given by $V_s = \frac{4}{3} \pi R^3 = \frac{4}{3

Vedclass · Accepted Answer

$126$

Vedclass · Answer

(A) The volume of the metallic sphere with diameter $21\,cm$ (radius $R = 10.5\,cm$ or $21/2\,cm$) is given by $V_s = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (\frac{21}{2})^3 = \frac{4}{3} \pi 	imes \frac{9261}{8} = \frac{3087}{2} \pi \, cm^3$.The volume of one cone with diameter $7\,cm$ (radius $r = 3.5\,cm$ or $7/2\,cm$) and height $h = 3\,cm$ is given by $V_c = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (\frac{7}{2})^2 	imes 3 = \pi 	imes \frac{49}{4} = 12.25 \pi \, cm^3$.The number of cones $n$ is calculated as $n = \frac{V_s}{V_c} = \frac{3087 \pi / 2}{49 \pi / 4} = \frac{3087}{2} 	imes \frac{4}{49} = \frac{3087 	imes 2}{49} = 63 	imes 2 = 126$.Thus,$126$ cones can be produced.

How many cones with diameter $7\,cm$ and height $3\,cm$ can be produced by melting a metallic sphere with diameter $21\,cm$?

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