A sphere of radius 2cms is dropped into a cylinder of radius 4 cms containing…
2023
A sphere of radius 2cms is dropped into a cylinder of radius 4 cms containing water upto 2.2cms. The raise in the water level is?
- A.
0.67 cms
- B.
0.90 cms
- C.
0.77 cms
- D.
0.80 cms
Attempted by 2 students.
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Correct answer: A
Answer: 2/3 cm (≈ 0.67 cm)
Compute the volume of the sphere with radius 2 cm: V_sphere = (4/3)πr^3 = (4/3)π(2^3) = (32/3)π cm³.
Compute the cross-sectional area of the cylinder with radius 4 cm: A_cylinder = πR^2 = π(4^2) = 16π cm².
Equate the displaced water volume to the sphere volume. The rise in water height h satisfies A_cylinder × h = V_sphere, so h = V_sphere / A_cylinder.
Substitute the values: h = ((32/3)π) / (16π) = (32/3) ÷ 16 = 32 / (3×16) = 2/3 cm ≈ 0.67 cm.
Therefore the rise in the water level is 2/3 cm (approximately 0.67 cm).