How many cones equal one cylinder (same r and h): A right circular cylinder is completely filled with water. How many right circular cones with the same radius and height are needed to store the same water?

Introduction / Context:This tests the known volume relationship between a cylinder and a cone with identical radius and height. It is a standard ratio result used often in mensuration.

Given Data / Assumptions:

• Same radius r and height h for both solids.
• V_cylinder = π r^2 h; V_cone = (1/3) π r^2 h.

Concept / Approach:

• Compare the formulas to find how many cones equal one cylinder.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 2/4/5: Do not match the derived exact ratio of 3.

Common Pitfalls:

• Using 1/2 instead of 1/3 for the cone volume.
• Forgetting the factor 1/3 attached to the cone formula.

Final Answer:

3