**AP Calculus BC Question 165: Answer and Explanation**

### Test Information

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**Question: 165**

**2.**

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

**Explanation:**

(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.