Geometry and TrigonometryHardEqual volumes, different radii
Geometry and Trigonometry practice question
Cylinder A has a radius of 2 and a height of 9. Cylinder B has a radius of 3 and the same volume as cylinder A. What is the height of cylinder B?
Answer: 4
Volume of A: π(2²)(9) = 36π. For B: π(3²)h = 9πh = 36π, so h = 4.
Common wrong answers
- If you answered 6
- 6 scales the height by 2/3 (the ratio of radii). Volume depends on the radius SQUARED, so the height scales by 4/9.
- If you answered 36
- 36 is the volume divided by π, not the height.
- If you answered 13.5
- 13.5 scales the height UP by 3/2; a larger radius needs a smaller height for the same volume.
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