Effect on cylinder volume when height changes: If a cylinder’s height decreases by 8% while its radius is unchanged, by what percentage does its volume change?

Introduction / Context:
Volume of a cylinder is V = πr^2h. When only one dimension changes, the percentage change in V equals the percentage change in that dimension’s factor (holding r constant). This is an application of proportional reasoning.

Given Data / Assumptions:

• r unchanged
• h decreases by 8% → new h = 0.92h
• V_new = πr^2 * (0.92h) = 0.92 * V_old

Concept / Approach:
Because V is directly proportional to h (with r fixed), the volume decreases by the same 8%. No computation with π or r is needed beyond recognizing proportionality.

Step-by-Step Solution:
V_old = πr^2hV_new = πr^2 * (0.92h) = 0.92 V_oldPercentage decrease = (1 − 0.92) * 100% = 8%

Verification / Alternative check:
Try numbers: let r = 1, h = 100. V_old = 100π. New h = 92 → V_new = 92π. Decrease = 8π out of 100π = 8%.

Why Other Options Are Wrong:
4% and 6% understate; 10% overstates; 12% is unrelated. Only 8% matches the direct dependence on h.

Common Pitfalls:
Thinking area or volume changes require squaring or cubing in every case; here only height changes, so the effect is linear and equal to 8%.

Final Answer:
8%