Question

A cylindrical container having diameter 16 cm and height 40 cm is full of ice cream. The ice-cream is to be filled into comes of height 12cm and diameter 4cm having a hemispherical shape on the top. Find the number of such cones which can be filled with Ice cream.

Answer 1

Volume of cylindrical container$=\pi \times r^2\times h$

where $r=\frac{16}{2}=8cm$ and $h=40cm$

Volume of cylindrical container$=\pi \times 8^2\times 40=2560\times \pi c{m}^3$

Volume of ice-cream cone $=$ Volume of cone $+$ volume of hemisphere $=\frac{\pi \times r^2\times h}{3}+\frac{2\times \pi \times r^3}{3}$

Here $r=\frac{4}{2}=2cm$ and $h=12cm$

Volume of ice-cream cone $=\frac{\pi \times 2^2\times 12}{3}+\frac{2\times \pi \times 2^3}{3}$

Volume of ice-cream cone $=21.33\times \pi c{m}^3$

Number of cones $=\frac{\text{Volume of cylindrical container}}{\text{Volume of cone}}=\frac{2560\times \pi c{m}^3}{21.33\times \pi c{m}^3}=120$

Hence number of cones $=120$