1. Volumes by Slicing

I've been working on this problem for about half an hour and haven't gotten anywhere.

The base of a solid is the region between the curve y=2sqrt[sinx] and the interval [0, pi] on the x-axis. The cross-sections perpendicular to the x-axis are equilateral triangles with bases running from the x-axis to the curve.

I think I'm supposed to use the formula V=A(x)dx, need help, thanks.

2. Originally Posted by leticiamc08
I've been working on this problem for about half an hour and haven't gotten anywhere.

The base of a solid is the region between the curve y=2sqrt[sinx] and the interval [0, pi] on the x-axis. The cross-sections perpendicular to the x-axis are equilateral triangles with bases running from the x-axis to the curve.

I think I'm supposed to use the formula V=A(x)dx, need help, thanks.
$\displaystyle V = \int_a^b A(x) \, dx$

area of an equilateral triangle with side length $\displaystyle s$ is

$\displaystyle A = \frac{\sqrt{3}}{4} s^2$

$\displaystyle s = 2\sqrt{\sin{x}}$

set it up and find the volume.