Question

A container, shaped like a right circular cylinder of diameter 12 cm and height 15 cm, is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 6 cm with a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Answer 1

Diameter of the container = 12 cm
Thus, radius of the container = 6 cm
Height of the container = 15 cm

Volume of the container $={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times 6\times 6\times 15=1697.143{\mathrm{cm}}^3$

Height of a cone = 12 cm
Diameter of a cone = 6 cm
Radius of a cone = 3 cm
Volume of a cone $=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\times \frac{22}{7}\times 3\times 3\times 12=113.143{\mathrm{cm}}^3$
Volume of hemisphere$=\frac{2}{3}{\mathrm{\pi r}}^3=\frac{2}{3}\times \frac{22}{7}\times 3\times 3\times 3=56.571{\mathrm{cm}}^3$

Volume of ice-cream in each cone = $113.143+56.571=169.714c{m}^3$

Number of cones of required dimension that can be filled with the given ice-cream$=\frac{1697.143}{169.714}=10$