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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 $(\frac{1}{6})^{\text{th}}$ 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 = $\frac{1}{3}\times\pi\times9\times12=36\pi\text{cm}^3$
Volume of ice-cream in the cone = $\frac{5}{6} \times 36 \times \pi = 30\pi\text{cm}^3$
Volume of ice-cream on top = $\frac{2}{3} \times 27 \times \pi = 18\pi\text{cm}^3$
Total volume of the ice-cream = $(30\pi +18\pi) = 48\pi\text{cm}^3$
$=48\times3.14=150.72\text{cm}^3$
Volume of ice-cream in the cone = $\frac{5}{6} \times 36 \times \pi = 30\pi\text{cm}^3$
Volume of ice-cream on top = $\frac{2}{3} \times 27 \times \pi = 18\pi\text{cm}^3$
Total volume of the ice-cream = $(30\pi +18\pi) = 48\pi\text{cm}^3$
$=48\times3.14=150.72\text{cm}^3$