Question

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. Then number of such cones will be
(a) 21
(b) 63
(c) 126
(d) 130

Answer 1

(c) 126

Number of cones =$\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{sphere}}{\mathrm{volume}\mathrm{of}1\mathrm{cone}}$
$$\begin{gathered} =\frac{{\displaystyle \frac{4}{3}}\mathrm{\pi }\times 10.5\times 10.5\times 10.5}{{\displaystyle \frac{1}{3}}\mathrm{\pi }\times 3.5\times 3.5\times 3} \\ =4\times 3\times 3\times 3.5=126 \end{gathered}$$