Question

A right circular cylinder having a diameter $12cm$ and height $15cm$ is full of 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

We have
Radius of the cylinder $=6cm$
height of the cylinder $=15cm$
Volume of the cylinder $=\pi r^{2}h=\pi \times 6^2\times 15c{m}^3=540\pi c{m}^3$
Radius of the ice-cream cone$=12cm$
Height of the ice-cream cone $=12cm$

Volume of the conical part of ice-cream cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \times 3^2\times 12c{m}^3=36\pi c{m}^3$

Volume of the hemispherical top of the ice cream cone $=\frac{2}{3}\pi r^3=\frac{2}{3}\pi \times 3^3=18\pi c{m}^3$

total volume of the ice cream cone $(36\pi +18\pi )c{m}^3=54\pi c{m}^3$

Number of ice cream cones $=\frac{Volumeofthecylinder}{TotalVolumeofice-creamcone}=\frac{540\pi }{54\pi }=10$