11. The area bounded by the curve y² = 12x and the line x = 3 is revolved about the line x = 3. What is the volume generated?
A. 186 B. 179 C. 181 D. 184
12. Find the volume generated by revolving about the y-axis the area bounded by the curve y = x² + 4 and y = 2x².
A. 6pi B. 16pi/3 C. 7pi D. 8pi
13. The area enclosed by the ellipse 4x² + 9y² = 36 is revolved about the line x = 3, what is the volume generated?
A. 370.3 B. 360.1 C. 355.3 D. 365.1
14. Find the volume of the pentagon with given vertices at (1, 0), (2, 2), (0, 4), (-2, 2), (-1, 0) if it is revolve about the x-axis.
A. 98pi/5 B. 36pi C. 104pi/3 D. 72pi
15. Find the coordinates of the centroid of the plane area bounded by the parabola y = 4 - x² and the x-axis.
A. (0, 1.5) B. (0, 1) C. (0, 2) D. (0, 1.6)
16. Find the center of mass of homogenous lamina bounded by the following curves: x = 2y, x = y² + 1, y = 0.
A. (3/5, 1/3) B. (4/5, 1/4) C. (2/3, 3/5) D. (1/4, 2/5)
17. Find the centroid of the volume generated by revolving about the y-axis the area bounded by the curve y² = 4ax in the first quadrant and the line x = a.
A. 3/2 a B. 5/6 a C. 4/5 a D. 3/4 a