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Find the volume of solid generated when the area enclosed...

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

View answer & explanation

Correct answer is B

$y = 2x \\ V = \int\pi^{2}dy \\ but\hspace{1mm}y = 2x \\ V = \int\pi4x^{2}dx\\ V = \frac{4(3)^{3}\pi}{3}-\frac{4(3)^{3}\pi}{3}\\V=\frac{4*27\pi}{3} = 36\pi \hspace{1mm}cubic\hspace{1mm}units$

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