AP Calculus BC Question 165: Answer and Explanation

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Question: 165


The region S in the figure above is bounded by y = sec x and y = 4. What is the volume of the solid formed when S is rotated about the x-axis?

  • A. 108.177
  • B. 39.867
  • C. 53.126
  • D. 54.088

Correct Answer: A


(A) S is the region bounded by y = sec x, the y-axis, and y = 4.

We send region S about the x-axis. Using washers, Δ V = π(R2 - r2) Δx. Symmetry allows us to double the volume generated by the first-quadrant portionof S. So for V we have

A calculator yields 108.177.