Question

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

Answer 1

R.E.F image

$U=\pi r^{2}h$

$=\pi 6\times 6\times 15$

$=540\pi c{m}^3$

$U=V_{hemisphere}+V_{cone}$

$=\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^2\left(4r\right)$

$=\frac{2}{3}\pi r^3+\frac{4}{3}\pi r^3$

$=2\pi r^3$

$\therefore 540=10\times 2\pi \times r^3$

$27=r^3$

$r=3cm$

$U_{cylinder}=\pi r^{2}h$

$U_{hemisphere}=\frac{2}{3}\pi r^3$

$V_{cone}=\frac{1}{3}\pi r^{2}h$