Finding Volume by Cross Section Area

[heather7113]

I need to find the volume of this figure y=sinx, y=sinx + 2, x=4, x=-4 using the area of triangular cross sections. i don't really know where to start...how to find the formula for area of cross section etc. HELP!

 

[LCKurtz]

I need to find the volume of this figure y=sinx, y=sinx + 2, x=4, x=-4 using the area of triangular cross sections. i don't really know where to start...how to find the formula for area of cross section etc. HELP!

What kind of triangle cross sections? Right? Equilateral? Have you drawn a sketch of this? Do you know the formula for the area of a triangle? A sketch will help.

 

[heather7113]

The cross sections are equilateral triangles. And I have drawn a sketch - I'm just not sure what the integral should be - like what is the formula for the base of the triangle. I know the formula is sgrt 3 x b / 4 I just don't really know what to plug in and what the numbers should be...?

 

[LCKurtz]

The cross sections are equilateral triangles. And I have drawn a sketch - I'm just not sure what the integral should be - like what is the formula for the base of the triangle. I know the formula is sgrt 3 x b / 4 I just don't really know what to plug in and what the numbers should be...?

Isn't the base of the triangle just the positive difference between the values of the two curves at position x? And the slice has thickness dx. At least that is so on the interval (0,\pi). Outside of that interval you have to be careful because the curves cross each other at 0 and \pi.

 

[heather7113]

Thanks. Thats what I was thinking, I just wasn't sure...