Question

A cylindrical container having a diameter of $16$ cm and a height of $40$ cm is full of ice cream. The ice cream is to be filled into cones of height $12$ cm and diameter $4$ cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Answer 1

Radius of cylinder $=r=8$ cm
Height of cylinder $=h=40$ cm
Volume of cylinder $=\pi r^{2}h=\pi \times (8{)}^2\times 40$
Ice-cream inside the cylinder $=\pi \times (8{)}^2\times 40$ ........ (i)
Radius of cone $=r=2$ cm
Height of cone $=h=12$ cm
Volume of cone $=\frac{\pi }{3}{r}^{2}h=\frac{\pi }{3}\times (2{)}^2\times 12=16\pi$
Radius of hemisphere $=r=2$ cm
Volume of hemisphere $=\frac{2}{3}\pi r^3=\frac{2}{3}\times \pi \times (2{)}^3=\frac{16}{3}\pi$
Ice-cream in one cone $=$ Volume of cone + Volume of hemisphere $=16\pi +\frac{16}{3}\pi =\frac{64}{3}\pi$
Number of cones which can be filled with ice-cream $=\frac{\text{Ice-cream inside the cylinder}}{\text{Ice-cream in one cone}}$
$=\frac{\pi \times (8{)}^2\times 40}{\frac{64}{3}\pi }$
$=120$