Question

A solid metallic spherical ball of radius 28cm is melted down and recast into small cones.If the diameter of the base of the cone is 28cm and the height is 4cm find the number of such cones can be made

Answer 1

Let the no. of Cones be x.

Since a sphere is melted and then cast into no. of cone then $\underline{volume\:of\:solid\:spherical\:ball\:will\:be\:equal\:to\:volume\:of\:n\:cones}$

$volume \: of \: spherical \: ball = \frac{4}{3} \pi \: {(28)}^{3} \\ volume \: of \: n \: cones = n \frac{1}{3} \pi {(28)}^{2} \times 4 \\ \\ since \: volumes \: are \: equal \: so \\ \\ \frac{4}{3} \pi \: {(28)}^{3} = \frac{n}{3} \pi \: {(28)}^{2} \times 4 \\ n = 28$

$\boxed{\blue{no.\:of\:cones\:formed\:is\:28}}$