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A metal sphere of radius 36 cm is immersed in a cylindrical vessel that is partially filled with water. The diameter of the vessel is 4.8 m. If the sp
Question

A metal sphere of radius 36 cm is immersed in a cylindrical vessel that is partially filled with water. The diameter of the vessel is 4.8 m. If the sphere is completely submerged in the water, find the rise in the water level.

A.

1.82 cm

B.

2.82 cm

C.

2.08 cm

D.

1.08 cm

Correct option is D

Given:
Radius of the metal sphere = 36
Diameter of the cylindrical vessel = 4.8 meters = 480 cm
Radius of the cylindrical vessel = 240
Formula Used:
Volume of sphere = 43×π×r3 \frac{4}{3} × π × r^3​​
Volume of cylinder = π × R^2 × h
Solution:
The volume of the water displaced will be equal to the volume of the completely submerged sphere.
Volume of sphere =  43×π×363\frac{4}{3} × π × 36^3​​

Volume of sphere = 43×π×46656 \frac{4}{3} × π × 46656​​
Volume of sphere = 62208 × π
Let the rise in the water level be h.
Volume of displaced water in the cylinder =  π×2402×hπ × 240^2 × h​​
Volume of displaced water = 57600 × π × h
Equate the volumes.
57600 × π × h = 62208 × π
h =  6220857600\frac{62208}{57600}​​

h = 108100\frac{108}{100}​​
h = 1.08
Final Answer
So the correct answer is (d)

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