A prism and a pyramid have the same base area and the same height. What is the ratio of the volume of the prism to that of the pyramid?
Aptitude
Volume and Surface Area
Difficulty: Easy
Choose an option
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A1 : 1
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B1 : 3
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C3 : 1
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DCannot be determined
Answer
Correct Answer: 3 : 1
Explanation
Introduction / Context:Comparing volumes of solids with the same base and height is a classic geometry result. Pyramids (including cones) have one-third the volume of the corresponding prism (or cylinder) with equal base and height.
Given Data / Assumptions:
- Same base area B and same height H.
Concept / Approach:Volume formulas: V_prism = B * H; V_pyramid = (1/3) * B * H. Take their ratio.
Step-by-Step Solution:
V_prism / V_pyramid = (B*H) / [(1/3)B*H] = 3Therefore, ratio = 3 : 1Verification / Alternative check:Analogy: Cylinder vs cone with same base and height also yields 3:1 for volumes.
Why Other Options Are Wrong:
- 1:1 and 1:3 contradict the standard formula.
- Cannot be determined: Sufficient information is provided via general formulas.
Common Pitfalls:Mixing up the factor 1/3 for pyramids and cones; thinking perimeter rather than area influences the ratio.
Final Answer:3 : 1