A right circular cylinder having diameter 12 cm and height 15 cm

Question:

A right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in 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.

Solution:

We have to find the number of cones which can be filled using the ice cream in the cylindrical vessel.

Radius of the cylinder $\left(r_{1}\right)=6 \mathrm{~cm}$

Height of cylinder $(h)=15 \mathrm{~cm}$

Radius of cone and the hemisphere on it $\left(r_{2}\right)=3 \mathrm{~cm}$

Height of cone $(l)=12 \mathrm{~cm}$

Let ‘n’ number of cones filled. So we can write it as,

$n($ Volume of each cone $)=$ Volume of cylinder

So,

$(n)\left(\frac{1}{3} \pi r_{2}^{2} l+\frac{2}{3} \pi r_{2}^{3}\right)=\pi r_{1}^{2} h$

$(n)\left(\frac{r_{2}^{2}\left(l+2 r_{2}\right)}{3}\right)=r_{1}^{2} h$

Now put the values to get,

$(n)\left(\frac{9(12+6)}{3}\right)=36(15)$

$54 n=540$

Therefore, $n=10$

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