Question
Let D represent the region bounded by the unit circle centered at the origin. Find the volume of the solid obtained by revolving D about the line x = 2.
(A)\(\frac{8\pi }{3}+4\pi ^{2}\)
(B) \(\frac{2\pi }{3}+\pi ^{2}\)
(C) \(\pi \left ( \frac{4}{3} +\sqrt{2}\right )\)
(D) \(\frac{8\pi }{3}\)
Answer/Explanation
Ans:(A)
Question
What is the volume of the solid generated by rotating about y = -1 the region in the first quadrant bounded by the curves y = 3 – x and \(y=\frac{x}{2}\) ?
(A) \(\frac{7\pi }{3}\)
(B) \(\pi \left [ \frac{7}{3} -\pi \ln 4\right ]\)
(C) \(\pi \left [ \frac{9}{2}+\ln 3 \right ]\)
(D) \(\pi \left [ \frac{10}{3}-4\ln 2 \right ]\)
Answer/Explanation
Ans:(D)
