Question

A cylindrical container whose diameter is 12 cm and height is 15 cm is filled with ice cream. The whole ice cream is distributed to 10 children in equal cones having a hemispherical top. If the height of the conical portion is twice the diameter of its base then find the diameter of the ice cream cone.

Answer 1

Cylinder

Volume
$144\times \frac{22}{7}\times 15$
=2160 sq.cm
is distributed in 10 cones
$\therefore$ Volume of one ice-cream cone = 216 sq.cm
Volume of top hemisphere

$=\frac{2}{3}\pi {\left(\frac{d}{2}\right)}^3=\frac{\pi d^3}{12}$
Volume of conical portion
$=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\pi {\left(\frac{d}{2}\right)}^2$
$=\frac{\pi d^3}{6}$
V (ice cream cone) = =\frac{\pi d^3}{12} + =\frac{\pi d^3}{6} . \frac{3}{12} . \pi d^3\)
$\therefore \frac{\pi d^3}{4}=216\pi$
$\therefore d^3=\sqrt{4\times 216}=\sqrt[3]{3864}$
$=\sqrt[3]{33^3\times 2^3\times 2^2}=6\times \sqrt[3]{34}$
$\simeq 9.524cm$