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Translate a rotation axis before integrating

Curve CC is y=3x/(4−x)y=\sqrt{3x/(4-x)}, 0≤x<40\le x<4. Region RR is bounded by CC, y=3y=3 and the y-axis. It rotates through 2π2\pi about y=3y=3. Write the equation after translating CC three units down, and hence find the solid volume.

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Curve y=square root of 3x/(4 minus x) starts at the origin and meets the horizontal rotation axis y=3 at (3,3); x=4 is a vertical asymptote. Region R is shaded between y=3, the curve and the y-axis from x=0 to x=3.
Curve y=square root of 3x/(4 minus x) starts at the origin and meets the horizontal rotation axis y=3 at (3,3); x=4 is a vertical asymptote. Region R is shaded between y=3, the curve and the y-axis from x=0 to x=3.
Curve y=square root of 3x/(4 minus x) starts at the origin and meets the horizontal rotation axis y=3 at (3,3); x=4 is a vertical asymptote. Region R is shaded between y=3, the curve and the y-axis from x=0 to x=3.

[2016/RVHS/II/4(modified)]

CJC · Discussion · Question 9

Translate both the curve and the axis so the new axis is y=0.

Read the worked solution