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?
Aptitude
Volume and Surface Area
Difficulty: Easy
Choose an option
-
A2
-
B3
-
C4
-
D5
Answer
Correct Answer: 3
Explanation
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:
V_cylinder / V_cone = (π r^2 h) / ((1/3) π r^2 h) = 3.Therefore, 3 cones of the same r and h equal the cylinder volume.Verification / Alternative check:
Pick any r,h (e.g., r=1, h=1): V_cyl=π; V_cone=π/3; three cones give π.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