Question

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.

Answer 1

Volume of metallic sphere would be same as total volume of the cones formed.

$\frac{4}{3} \pi {r}^{3} = n \: \frac{1}{3} \pi {r}^{2} h \\ 4 ({10.5})^{3} = n ( {1.75)}^{2} 3 \\ \frac{4}{3} ( {10.5})^{3} \times \frac{1}{ ({1.75)}^{2} } = n$
so, n=27.48 , which means 27 cones would be prepared from that metallic sphere.



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