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$504$ cones, each of diameter $3.5\ cm$ and height $3\ cm$, are melted and recast into a metallic sphere, Find the diameter of the sphere and hence find its surface area.
Given: 504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere
To do: Find the diameter of the sphere and hence find its surface area.
Solution:
No. of cones $= 504$
Diameter of a cone $= 3.5\ cm$
Radius of the cone, $r = \frac{3.5}{2}=1.75\ cm$
Height of the cone, $h = 3\ cm$
Volume of the cone $=\frac{1}{3} \pi r^{2} h$
$=\frac{1}{3} \pi \times ( 1.75^{2} \times 3$
$=3.0625\pi\ cm^{2}$
Volume of 504 cones $=504\times 3.0635\pi\ cm^{2}$
Let the radius of the new sphere be ‘R’.
Volume of the newly formed sphere$=\frac{4}{3} \pi R^{2}$
Volume of 504 cone$=$Volume of newly formed sphere
$3.0625\pi=\frac{4}{3} \pi R^{2}$
$\Rightarrow \ R^{2} =$
Radius of the new sphere $= 10.5\ cm$
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