Question

A right circular cylinder having diameter $12cm$ and height $15cm$, is full of ice cream. The ice cream is to be filled in identical cones of height $12cm$ and diameter $6cm$ having a hemispherical shape on the top. Find the no. of cones required.

Answer 1

Volume of cylinder $=\pi r^{2}h$

$=\pi (6{)}^2\times 15$

$=540\pi$

Volume of ice cream cone $=$ Volume of cone $+$ Volume of hemisphere

$=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3$

$=\frac{1}{3}\pi \times (3{)}^2\times 12+\frac{2}{3}\pi \times (3{)}^3$

$=36\pi +18\pi$

$=54\pi$

Now,

Number of cones $=\frac{Volumeofcylinder}{Volumeoficecreamcone}$

$=\frac{540\pi }{54\pi }$

$=10$

So, number of cones is 10.