Cylinder vs cone volume (same base radius and height): A cylinder and a cone share the same radius and height. Find the ratio of their volumes (cylinder : cone).

Introduction / Context:
This is a direct ratio comparison using standard volume formulas for solids sharing the same base and height.

Given Data / Assumptions:

• Cylinder volume V_cyl = πr^2h
• Cone volume V_cone = (1/3)πr^2h

Concept / Approach:
Compute V_cyl : V_cone = (πr^2h) : ((1/3)πr^2h) = 1 : 1/3 = 3 : 1.

Step-by-Step Solution:
V_cyl : V_cone = (πr^2h) : ((1/3)πr^2h) = 3 : 1

Verification / Alternative check:
Pick r = h = 1 for a numerical check: cylinder 1π; cone (1/3)π → ratio 3 : 1.

Why Other Options Are Wrong:
1:3 reverses the order; 1:2 and 2:1 do not match the 1/3 factor; 2:3 is arbitrary.

Common Pitfalls:
Forgetting the 1/3 in cone volume; mixing up which solid is first in the ratio.

Final Answer:
3 : 1