A conical flask of base radius r and height h is full of water. The water is poured into a cylindrical flask whose base radius is m·r. What is the height of water in the cylinder?

Introduction / Context:
Equate the cone’s volume to the cylinder’s volume to find the resulting water height. Work symbolically in terms of r, h, and m to derive a general formula.

Given Data / Assumptions:

• V_cone = (1/3)πr^2h.
• V_cyl = π(mr)^2 * H = πm^2 r^2 H, where H is required height.

Concept / Approach:
Set (1/3)πr^2h = πm^2 r^2 H and solve for H; cancel common factors π and r^2 (r ≠ 0).

Step-by-Step Solution:

Verification / Alternative check:
Dimensional check: H has units of h (length) divided by dimensionless m^2, so units are consistent.

Why Other Options Are Wrong:
They invert or misplace m or the factor 1/3 from cone volume.

Common Pitfalls:
Forgetting the 1/3 factor in the cone volume; not squaring m in the cylinder’s base area.

Final Answer:
h/(3 m^2)