Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.
A
81 π cubic units
B
36 π cubic units
C
18 π cubic units
D
9 π cubic units
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(y = 2x \\ V = \int\pi y^{2}dy \\ but\hspace{1mm}y = 2x \\ V = \int\pi4x^{2}dx\\ V = \frac{4(3)^{3}\pi}{3} - \frac{4(0)^{3}\pi}{3}\)
V = \(\frac{4*27\pi}{3}\) = 36\(\pi \hspace{1mm}cubic\hspace{1mm}units\)
(Note: the limit of integration x = 0 → x = 3)
Source: Myschool Past Questions Archive (Record #544)