Geometry and TrigonometryVery hardCone and cylinder with the same base and height
Geometry and Trigonometry practice question
A cone and a cylinder have the same base radius, 3, and the same height, 4. How many times must the cone be filled with water and emptied into the cylinder to fill the cylinder exactly?
Answer: 3
A cone's volume is one third of the volume of the cylinder with the same base and height: (1/3)πr²h versus πr²h. So it takes 3 cones to fill the cylinder. (With r = 3 and h = 4: cylinder 36π, cone 12π.)
Common wrong answers
- If you answered 1
- The cone holds only a third as much as the cylinder, so one fill leaves it two-thirds empty.
- If you answered 9
- 9 is 3², perhaps from squaring the radius. The ratio of the volumes is exactly 3, regardless of the dimensions.
- If you answered 12
- 12 is the cone's volume divided by π (12π), not the number of fills.
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