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?

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:

Verification / 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