A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into m toys each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of n is:

Volume of cylinder = $$\pi \times r^2 \times h = \pi \times 12^2 \times 15 = 2160 \pi$$

Volume of n right circular cone = $$ \frac{1}{3}\pi \times r^2 \times h \times m =  \frac{1}{3}\pi \times 3^2 \times 9 \times n$$

Volume of hemisphere = $$ \frac{2}{3} \pi r^3 \times m =  \frac{2}{3} \pi \times 3^3 \times n$$

volume of cylinder = Volume of n right circular cone + Volume of n hemisphere

$$2160 \pi =  \frac{1}{3}\pi \times 3^2 \times 9 \times n + \frac{2}{3} \pi 3^3 \times n$$

2160 = 27n + 18n

n = 2160/45 = 48