Question

A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream is to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice cream cone.

• A. 4.5 cm
• B. 3 cm
• C. 6 cm
• D. 1.5 cm

Answer 1

The correct option is B

3 cm

$Numberofcones=\frac{Volumeoficecreamincylinder}{Volumeofcone+Volumeofhemisphere}$
$\begin{array}{cc}\Rightarrow & 10=\frac{\pi r^{2}H}{\frac{1}{3}\pi r^{2}h+\frac{2}{3}}\pi r^3\\ \Rightarrow & 10=\frac{\pi (6{)}^2\times 15}{\frac{\pi r^2}{3}(h+2r)}=\frac{6\times 6\times 15}{\frac{r^2}{3}(4r+2r)}\\ & [\because Heightconicalportionisfourtimestheradiusofitsbase]\\ \Rightarrow & 20r^3=90\times 6\\ \Rightarrow & r^3=27\Rightarrow r=3cm\end{array}$
$\therefore$ Radius of the ice cream cone = 3 cm