Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.
- 81 π cubic units
-
36 π cubic units
- 18 π cubic units
- 9 π cubic units
The correct answer is: B
Explanation
\(y = 2x \\ V = \int\pi^{2}dy \\ but\hspace{1mm}y = 2x \\ V = \int\pi4x^{2}dx\\ V = \frac{4(3)^{3}\pi}{3}-\frac{4(3)^{3}\pi}{3}\\V=\frac{4*27\pi}{3} = 36\pi \hspace{1mm}cubic\hspace{1mm}units\)