Cone — If only the height of a right circular cone is doubled while radius is unchanged, by what percentage does its volume increase?

Introduction / Context:Volume of a cone V = (1/3) * π * r^2 * h. If r is fixed and h changes, the volume scales linearly with h.

Given Data / Assumptions:

• r is constant
• h → 2h
• V ∝ h (with r fixed)

Concept / Approach:Double h ⇒ double V. A doubling corresponds to an increase of 100% (since new is 2× original).

Step-by-Step Solution:Original V = (1/3)πr^2hNew V' = (1/3)πr^2(2h) = 2 * VPercentage increase = (2 − 1) * 100% = 100%

Verification / Alternative check:Pick numbers: r = 1, h = 3 ⇒ V = π; double h to 6 ⇒ V = 2π (exactly twice).

Why Other Options Are Wrong:200% or 300% imply 3× or 4× total; 400% is 5×; 50% is only 1.5×, not correct.

Common Pitfalls:Forgetting that only height changes; mixing up with r scaling (which affects r^2).

Final Answer:100%