A right circular cylinder having diameter 12 cm and height 15 cm

We have to find the number of cones which can be filled using the ice cream in the cylindrical vessel.

Radius of the cylinder $\left(r_{1}\right)=6 \mathrm{~cm}$

Height of cylinder $(h)=15 \mathrm{~cm}$

Radius of cone and the hemisphere on it $\left(r_{2}\right)=3 \mathrm{~cm}$

Height of cone $(l)=12 \mathrm{~cm}$

Let ‘n’ number of cones filled. So we can write it as,

$n($ Volume of each cone $)=$ Volume of cylinder

So,

$(n)\left(\frac{1}{3} \pi r_{2}^{2} l+\frac{2}{3} \pi r_{2}^{3}\right)=\pi r_{1}^{2} h$

$(n)\left(\frac{r_{2}^{2}\left(l+2 r_{2}\right)}{3}\right)=r_{1}^{2} h$

Now put the values to get,

$(n)\left(\frac{9(12+6)}{3}\right)=36(15)$

$54 n=540$

Therefore, $n=10$