Volume of Solid: Frustum of Right Circular Cone

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Homework Statement


Find the volume of the solid S.

A frustum of a right circular cone with height h, lower base radius R, and top radius r.



Homework Equations


the integral of (pi)(r^2) [top] - (pi)(r^2) [bottom] dx


The Attempt at a Solution


I don't know how to start. I know I need to find the endpoints where the cross sections meet, but I'm not sure how to go about that.
 
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Divide the frustrum into circles of thickness dy. The area of the circle will be a function of y. Integrate to find the volume.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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