Question

A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to make n solid cones of height 1 cm and base radius 1 mm. The value of n is
(a) 450
(b) 1350
(c) 4500
(d) 13500

Answer 1

(d) 13500
Radius of the cylinder = 3 cm
Height of the cylinder = 5 cm
Radius of the cone = 1 mm = 0.1 cm
Height of the cone = 1 cm

∴ Number of cones, n = $\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}}{\mathrm{volume}\mathrm{of}1\mathrm{cone}}$
$$\begin{gathered} =\frac{\mathrm{\pi }\times 3^2\times 5}{{\displaystyle \frac{1}{3}}\mathrm{\pi }\times 0.1^2\times 1} \\ =\frac{3\times 9\times 5}{0.01} \\ =13500 \end{gathered}$$