Cone-to-cylinder water transfer with π = 22/7: A cone of radius 3.5 cm and height 27 cm is full of water. The water is poured into a cylinder of radius 2.1 cm. Find the height (in cm) of water in the cylinder. (Use π = 22/7.)

Introduction / Context:Volumes are conserved when a fluid is transferred. Set the cone’s volume equal to the cylinder’s volume and solve for the cylinder’s height using π = 22/7 for tidy arithmetic with the given radii.

Given Data / Assumptions:

• Cone: r = 3.5 cm, h = 27 cm, V_cone = (1/3)πr^2h.
• Cylinder: R = 2.1 cm, height H unknown, V_cyl = πR^2H.
• π = 22/7.

Concept / Approach:Equate (1/3)πr^2h = πR^2H and cancel π. Compute numerically with exact fractions to avoid rounding.

Step-by-Step Solution:

Verification / Alternative check:Reverse: 13.86 * 25 = 346.5, matches the cone’s volume.

Why Other Options Are Wrong:12.5, 37.5, 50, 30 do not satisfy volume equality with the given radii.

Common Pitfalls:Forgetting the 1/3 in the cone volume or using diameter instead of radius.

Final Answer:25 cm