Cylinder with unchanged radius — percent change in volume when height increases: If the height of a right circular cylinder is increased by 17.5% while the radius remains unchanged, by what percent does its volume increase?

Introduction / Context:For a cylinder, volume V = πr^2h. If r is constant, volume varies directly with h. Therefore, any percentage change in height translates identically to volume.

Given Data / Assumptions:

• r = constant
• h increases by 17.5%
• V ∝ h (with r fixed)

Concept / Approach:Because r is unchanged, V_new / V_old = h_new / h_old = 1.175. The percentage increase in V equals 17.5%.

Step-by-Step Solution:V_old = πr^2hV_new = πr^2(1.175h) = 1.175V_oldPercent increase = (1.175 − 1)*100% = 17.5%

Verification / Alternative check:Pick r = 1, h = 100 (units); volumes scale exactly like heights.

Why Other Options Are Wrong:18% and 19.8% are rounded or compounding misconceptions; 25% is unrelated.

Common Pitfalls:Trying to apply compound effects without any radius change; mixing area vs. volume changes.

Final Answer:17.5%