Question 108

A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is just completely submerged in water, then the rise of water level in the cylindrical vessel is

Solution

Since, the sphere is completely submerged in water, then volume of sphere = volume of cylinder.

Radius of sphere = 3cm and radius of cylinder = 6cm

Rise in the water level will be equal to the height of cylinder.

=> $$\frac{4}{3} \pi R^3 = \pi r^2 h$$

=> $$\frac{4}{3} * 3^3 = 6^2 h$$

=> $$h = \frac{4 * 9}{36}$$

=> $$h = 1$$ cm

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