Please help solving this question through Integration

[RBrish]

The sides of a triangle are 8,15,17.The triangle is rotated about its longest side.Find the volume of figure generated?

I've been able to solve this question by visualising a cone and using its properties,but I want to solve it through angular rotation and its integration like ∫Adθ from 0 to 2π.
Pls help me solve it .

 

[Dr.Peterson]

Sure. But you have to start.

Place the triangle on a coordinate plane, and identify what is being rotated about what axis. Then set up an integral. (It probably won't look like what you wrote.)

Once you've done that, we'll have something to talk about.

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[RBrish]

Hi !
Okay so if i place the triangle on the coordinate plane,I will know the equation of hypotenuse as 8y+15x+120=0.But I dont know how to proceed further as I studied Integration 8 years ago,and I'm not able to form the Integral Equation,especially when angular rotation is involved.
So pls help me with it.

 

[Dr.Peterson]

Well, if it's rotated about its longest side, then that would be the hypotenuse, which should be placed on the x-axis. You appear to be placing the 8 side on the x-axis, so you'll be finding a different volume.

Placed properly, the function you'll be integrating will be a "piecewise" function, consisting of two line segments.

Or when you said "longest side", did you mean "longer leg", knowing it's a right triangle?