Question

A cylindrical container of radius $6cm$ and height $15cm$ is filled with ice-cream. The whole ice cream has to be distributed to $10$ children in equal cones with hemispherical tops. The height of the conical portion is $4$ times the radius of its base, find the radius of the ice-cream cone.

• A. $3cm$
• B. $6cm$
• C. $12cm$
• D. $24cm$

Answer 1

The correct option is A $3cm$

Height of cylindrical container$=15cm$

Radius of cylindrical container$=6cm$

Volume of container$=\pi r^{2}h=3.14\times 6\times 6\times 15$

$=1695.6c{m}^3$

Quantity of ice cream each child gets $=\frac{1695.6}{10}=169.56c{m}^3$

Let radius of cone=r=radius of hemisphere

$\therefore$Height of cone$=4r$

Volume of hemisphere+volume of cone$=169.56c{m}^3$

$\Rightarrow \frac{2}{3}\pi r^3+\frac{1}{3}\pi r^{2}h=169.56$

$\Rightarrow \frac{2}{3}\times 3.14\times r^3+\frac{1}{3}\times 3.14\times r^2\times 4r=169.56$

$\Rightarrow 2.09r^3+4.18r^3=169.56$

$\Rightarrow 6.27r^3=169.56$

$\Rightarrow 6.27r^3=169.56$

$\Rightarrow r^3=\frac{169.56}{6.27}\approx 27$

$\Rightarrow r=3cm$

Therefore, radius of the ice cream cone is $3cm$