Question

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

Answer 1

Radius of cylinder = 6 cm, height of cylinder = 15 cm
Radius of cone = 3 cm, height of cone = 12 cm
Radius of hemispherical top on ice cream = 3 cm

Volume of cylinder
$=\pi r^{2}h$
$=\pi \times 6\times 6\times 15$
$=540\pi c{m}^3$

Volume of cone
$=\frac{1}{3}\times \pi \times 3^2\times 12$
$=36\pi c{m}^3$

Volume of hemisphere
$=\frac{2}{3}\pi r^3$
$=\frac{2}{3}\times \pi \times 3^3$
$=18\pi c{m}^3$
Volume of ice cream
$=(36+18)\pi$
$=54\pi c{m}^3$

$\Rightarrow \text{Number of ice creams}=\frac{\text{Volume of cylinder}}{\text{Volume of ice cream}}$
$=\frac{540\pi }{54\pi }=10$