Question

Right circular cylinder having diameter $12cm$ and height $15cm$ is full ice-cream. The ice-cream is to be filled in cones of height $12cm$ and diameter $6cm$ having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.

Answer 1

Given:

In right circular cylinder, $D=12cm\Rightarrow R=6cm$

Height $\left(H\right)=15cm$

The shape of the ice-cream is " Cone + hemisphere"

In which the measurements are $\left(d\right)=6cm\Rightarrow r=3cm$

height of the conical part $\left(h\right)=12cm$

Now,

Number of ice cream cones $=\frac{\text{volume of the circular cylinder}}{\text{Volume of cone+ Volume of hemi sphere}}$

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

$=\frac{\pi R^{2}H}{\frac{1}{3}\pi r^2(h+2r)}$

$=\frac{3R^{2}H}{r^2(h+2r)}$

$=\frac{3\left(6cm{)}^2\right(15cm)}{\left(3cm{)}^2\right(12cm+2\left(3cm\right))}$

$=\frac{3\times 36\times 15c{m}^3}{9\times 18c{m}^3}$

$=\frac{1\times 2\times 15}{3\times 1}$

$=10$

Therefore, required number of such cones which can be filled with ice-cream are $10$.