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An empty cone is of radius $3$ cm and height $12$ cm. Ice-cream is filled in it so that lower part of the cone which is $\left(\frac{1}{6}\right)^{\text{th}}$ of the volume of the cone is unfilled but hemisphere is formed on the top. Find volume of the ice-cream. (Take $\pi = 3.14$)
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Volume of the cone = $$\begin{aligned}& \frac{1}{3}\times\pi\times9\times12=36\pi \text{cm}^3 \\ & \text{Volume of ice-cream in the cone} = \frac{5}{6} \times 36 \times \pi = 30\pi \text{cm}^3 \\ & \text{Volume of ice-cream on top} = \frac{2}{3} \times 27 \times \pi = 18\pi \text{cm}^3 \\ & \text{Total volume of the ice-cream} = (30\pi +18\pi) = 48\pi \text{cm}^3 \\ & =48\times3.14=150.72\text{cm}^3\end{aligned}$$