A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is :

Solution (By Examveda Team)

$$\eqalign{ & {\text{Volume of cylinder :}} \cr & = \left( {\pi \times 3 \times 3 \times 5} \right)c{m^3} \cr & = 45\pi \,c{m^3} \cr & {\text{Volume of a cone :}} \cr & = \left( {\frac{1}{3}\pi \times \frac{1}{{10}} \times \frac{1}{{10}} \times 1} \right)c{m^3} \cr & = \frac{\pi }{{300}}\,c{m^3} \cr & \therefore {\text{Number of cones :}} \cr & = \left( {45\pi \times \frac{{300}}{\pi }} \right) \cr & = 13500 \cr} $$