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Question 71
A cylindrical vessel of radius 6 cm is partially filled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take π = 22/7)
Solution
Radius of sphere, R = 5 cm
Radius of cylinder, r = 6 cm and height of cylinder = h cm
The rise in water level is equal to the height of cylinder when volumes of both solids is equal.
=> Volume of cylinder = Volume of sphere
=> $$\pi r^2 h = \frac{4}{3} \pi R^3$$
=> $$(6)^2 \times h = \frac{4}{3} \times (5)^3$$
=> $$h = \frac{4 \times 125}{36 \times 3} = \frac{125}{27}$$
=> $$h = 4.63$$ cm
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