Rise in water level — A cylinder (diameter 60 cm) is partially filled. A sphere of diameter 60 cm is submerged. By how much does the water rise?

Introduction / Context:Water rise height h is found by equating displaced volume (sphere volume) to cylinder's additional water volume: πR^2 h = (4/3)πr^3.

Given Data / Assumptions:

• Cylinder radius R = 30 cm
• Sphere radius r = 30 cm
• Same π cancels

Concept / Approach:Compute h directly from the equality of volumes.

Step-by-Step Solution:πR^2 h = (4/3)πr^3 ⇒ h = (4/3) * r^3 / R^2h = (4/3) * 30^3 / 30^2 = (4/3) * 30 = 40 cm

Verification / Alternative check:Units are consistent (cm).

Why Other Options Are Wrong:15, 20, 25, 30 cm arise from halving or linear thinking rather than volume conservation.

Common Pitfalls:Using diameter in place of radius in formulas.

Final Answer:40 cm