Combined changes in radius and height – effect on volume: A cylinder’s radius decreases by 8% while its height increases by 4%. What is the net percentage change in volume?

Introduction / Context:Volume V = πr^2h. Independent percentage changes in r and h multiply as factors: r contributes quadratically (r^2), h linearly. This question checks compound percentage reasoning with multiplication of factors.

Given Data / Assumptions:

• r_new = 0.92r (8% decrease)
• h_new = 1.04h (4% increase)
• V_new / V_old = (0.92^2) * (1.04)

Concept / Approach:Compute the squared radius factor first, then multiply by the height factor, and finally convert to a percent change relative to 1 (100%).

Step-by-Step Solution:0.92^2 = 0.8464Overall factor = 0.8464 * 1.04 = 0.880256Percent change = (0.880256 − 1) × 100% = −11.9744%

Verification / Alternative check:Numerical sanity: a ~12% decrease is expected since the reduction in r^2 (≈ −15.36%) dominates the modest +4% height increase, yielding around −11.96%.

Why Other Options Are Wrong:Increase options contradict the computed factor < 1; 12.4678% refers to a different hypothetical combination; 8% is relevant only if h stayed constant.

Common Pitfalls:Adding percentages linearly (−16% + 4% = −12%) without squaring r; forgetting multiplicative compounding.

Final Answer:11.9744% (decrease)