Question 104

A sphere is cut into two hemispheres. One of them is used as bowl. It takes 8 bowlfuls of this to fill a conical vessel of height 12 cm and radius 6 cm. The radius of the sphere (in centimetre) will be

Solution

Height of cone = 12 cm and radius of cone = 6 cm

Let radius of hemisphere(or sphere) = $$r$$ cm

Now, 8 * volume of hemisphere = volume of cone

=> 8 * $$\frac{2}{3} \pi r^3 = \frac{1}{3} \pi * 6^2 * 12$$

=> $$r^3 = \frac{36 * 12}{16}$$

=> $$r = \sqrt[3]{27}$$ = 3 cm

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