Question

A container shaped like a right circular cylinder having diameter $12cm$ and height $15cm$ full of ice-cream. The ice cream is to be filled into 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

We know that,

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

Volume of cone $=\frac{1}{3}\pi r^{2}h$

Volume of hemisphere is $\frac{2}{3}\pi r^3$.

We have,
volume of ice-cream in the container shaped like a right circular cylinder having radius $6cm$ and height $15cm$

$=\pi \times 6^2\times 15{cm}^2$

volume of one ice-cream cones of height $12$ cm and diameter $6$ cm(shown in figure)

$=\{\frac{2}{3}\pi \times 3^3+\frac{1}{3}\pi \times 3^2\times 12\}{cm}^3=54\pi {cm}^3$

Let the total number of cones that can be filled with the ice-cream given in the container be $n$. Then
volume of ice-cream in $n$ cones $=$ volume of ice cream in the container

$\Rightarrow 54\pi \times n=\pi \times 36\times 15$

$\Rightarrow n=\frac{\pi \times 36\times 15}{54\pi }$

$=10$