The base of a solid is the region in the first quadrant bounded by , the -axis, and the -axis. Cross sections perpendicular to the -axis are squares. Find the volume of the solid.
Answer and explanation
Correct answer: A.
- Step 1: Cross sections perpendicular to the -axis have side length .
- Step 2: The area of each square cross section is .
- Step 3: The region extends from to (where ).
- Step 4: Integrate: .
- Step 5: Evaluate at limits: .
Answer
.
Why not the others: '1/3' computes ; '2/3' integrates ; '4/15' halves the true volume.
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