# Math Help - Surface Area of a Cycloid

1. ## Surface Area of a Cycloid

Find the surface area generated by revolving one arch of the cycloid about the x-axis.

Formula:
$2pi\int_{a}^{b}{y(t)}\sqrt{{x'(t)^2}+{y'(t)^2}} dt$

Thanks.

2. Originally Posted by jffyx
Find the surface area generated by revolving one arch of the cycloid about the x-axis.

Formula:
$2pi\int_{a}^{b}{y(t)}\sqrt{{x'(t)^2}+{y'(t)^2}} dt$

Thanks.
One arch is parametrised by $0 \leq t \leq 2 \pi$.

After doing the necessary differentiations, substituting and simplifying you get

$S = 2 \sqrt{2} \pi \int_0^{2 \pi} (1 - \cos t)^{3/2} \, dt$.