Question 78

A cylindrical vessel of radius 8 cm is partially filled with water. By how much will the water level rise if a sphere of radius 7 cm is completely immersed in this water?

Solution

Radius of sphere, R = 7 cm

Radius of cylinder, r = 8 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

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

=> $$(8)^2 \times h = \frac{4}{3} \times (7)^3$$

=> $$h = \frac{343}{16 \times 3} = 7.15$$ cm

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