Home / AP Calculus AB : 8.11 Volume with Washer Method: Revolving  Around the x- or y-Axis- Exam Style questions with Answer- MCQ

AP Calculus AB : 8.11 Volume with Washer Method: Revolving  Around the x- or y-Axis- Exam Style questions with Answer- MCQ

Question

A region in the first quadrant is enclosed by the graphs of  \(y=e^{2x}\),x = 1, and the coordinate axes.If the region is rotated about the y-axis, the volume of the solid that is generated is represented by which of the following integrals?

(A) \(2\pi\int_{0}^{1}xe^{2x}dx\)
(B)\(2\pi\int_{0}^{1}e^{2x}dx\)
(C)\(\pi\int_{0}^{1}e^{4x}dx\)
(D)\(\pi\int_{0}^{e}y ln ydy\)
(E)\(\frac{\pi }{4}\int_{0}^{e}ln^{2}ydy\)

▶️Answer/Explanation

Ans:A

Question

The volume of the solid obtained by revolving the region enclosed by the ellipse\( x^{2}+9y^{2}=9\) about the x-axis is
(A) 2π                        (B) 4π                         (C) 6π                 (D) 9π                         (E) 12π

▶️Answer/Explanation

Ans:B

Question

The region enclosed by the x-axis, the line x = 3, and the curve \(y=\sqrt{x}\) is rotated about the   x-axis. What is the volume of the solid generated?

(A)\(3\pi\)                 (B)\(2\sqrt{3\pi} \)                     (C)\(\frac{9}{2}\pi\)                         (D)\(9\pi\)                    (E)\(\frac{36\sqrt{3}}{5}\pi\)

▶️Answer/Explanation

Ans:C

Question

If the region enclosed by the y-axis, the line y =2 , and the curve \(y=\sqrt{x}\) is revolved about the y-axis, the volume of the solid generated is
(A) \(\frac{32π}{5}\)                        (B)  \(\frac{16π}{3}\)                                (C) \(\frac{16π}{5}\)                               (D) \(\frac{8π}{3}\)                                       (E) π

▶️Answer/Explanation

Ans:A

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