# Thread: Volume of a Solid ?

1. ## Volume of a Solid ?

Find the volume of the solid generated by revolving around the x-axis
the region bounded by the x-axis, and one arch of the cycloid
x = t−sint, y = 1−cost.
where 0 ≤ t ≤ 2pi.
[ Hint : Use the disk method and dV = piy2dx = piy2(dx/dt) dt ]

I'm confused on this problem. I think it's because I don't actually know what they're asking... Is y the upper and x (t-sint) the width?

2. Originally Posted by maxreality
Find the volume of the solid generated by revolving around the x-axis
the region bounded by the x-axis, and one arch of the cycloid
x = t−sint, y = 1−cost.
where 0 ≤ t ≤ 2pi.
[ Hint : Use the disk method and dV = piy2dx = piy2(dx/dt) dt ]

I'm confused on this problem. I think it's because I don't actually know what they're asking... Is y the upper and x (t-sint) the width?
$\displaystyle dV = \pi y^2 \, dx$ is the volume of a representative disk in terms of y and x.

$\displaystyle dV = \pi y^2 \cdot \frac{dx}{dt} \, dt = \pi(1-\cos{t})^2 \cdot (1-\cos{t}) \, dt$ is the same thing in terms of t since y and x are given in terms of t

$\displaystyle V = \pi \int_0^{2\pi} (1-\cos{t})^3 \, dt$

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# volume of cycloid about y axis

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