Rise in water level due to a submerged sphere: A cylinder of radius 4 cm contains water. A solid sphere of radius 3 cm is fully immersed. By how many cm does the water level rise?

Introduction / Context:Volume displaced equals the volume of the sphere. The rise in height equals displaced volume divided by the cylinder’s cross-sectional area. This checks volume formulas and unit consistency.

Given Data / Assumptions:

• Cylinder radius R = 4 cm ⇒ area A = π R^2 = 16π cm2
• Sphere radius r = 3 cm ⇒ volume V_sph = (4/3) π r^3 = (4/3) π * 27 = 36π cm3

Concept / Approach:

• Height rise h = displaced volume / area = V_sph / A.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 4.5 cm: Doubles the correct rise.
• 4/9 cm or 2/9 cm: Misplaced numerator/denominator during division.

Common Pitfalls:

• Using cylinder volume formula instead of area in the denominator.
• Forgetting to cube the sphere radius when computing volume.

Final Answer:

2.25 cm