Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.
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A.
81 π cubic units -
B.
36 π cubic units -
C.
18 π cubic units -
D.
9 π cubic units
Correct Answer: Option B
Explanation
(y = 2x \ V = intpi^{2}dy \ buthspace{1mm}y = 2x \ V = intpi4x^{2}dx\ V = frac{4(3)^{3}pi}{3}-frac{4(3)^{3}pi}{3}\V=frac{4*27pi}{3} = 36pi hspace{1mm}cubichspace{1mm}units)