Cylinder height from volume and base area: Find the height h of a right circular cylinder whose volume is 551 m^3 and whose base area is 36.5 m^2.

Introduction / Context:When the base area of a cylinder is known, its height follows directly from the volume relation V = (base area) * (height). This problem tests unit awareness and one-step algebra.

Given Data / Assumptions:

• Volume V = 551 m^3
• Base area A_base = 36.5 m^2
• Right circular cylinder; no rounding until the final step

Concept / Approach:Use the linear relation V = A_base * h, hence h = V / A_base. With consistent SI units, the quotient gives meters directly.

Step-by-Step Solution:h = V / A_base = 551 / 36.5 m36.5 * 15 = 547.5; remainder = 3.5 → h ≈ 15 + (3.5 / 36.5) ≈ 15.0959 mRounded sensibly, h ≈ 15.10 m (to 2 decimals)

Verification / Alternative check:Back-calculate V using h = 15.10 m: V ≈ 36.5 * 15.10 = 551.15 m^3, matching to rounding tolerance, confirming that the exact quotient is ~15.096 m.

Why Other Options Are Wrong:7 m, 10.5 m, and 14 m are far from 15.096 m when multiplied by 36.5. Since none listed equals ~15.10 m, the correct choice is “None of these.” The distractor 15.1 m (if shown) illustrates the correct magnitude but is not among the original options.

Common Pitfalls:Confusing diameter/radius formulas; mixing cm^2 with m^2; rounding too early leading to an option that seems to fit when it does not.

Final Answer:None of these