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Question 106
A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The entire ice-cream is divided equally among 10 children in the shape of cones surmounted by hemispherical tops. If the height of the conical ice-cream bow! is twice the diameter of its base, then the base radius of the cone is
Solution
Volume of ice cream in each cone = $$\frac{1}{10}\cdot\frac{22}{7}\cdot36\cdot15\ =\ \frac{33\cdot36}{7}$$
The ice cream is filled in the cone plus a surplus hemispherical lobe at top of it.
Hence,
$$\ \frac{33\cdot36}{7}=\frac{1}{3}\cdot\frac{22}{7}\cdot r^2\cdot4r\ +\ \frac{2}{3}\cdot\frac{22}{7}\cdot r^3$$
Solving this, we easily get r = 3
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