(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A solid has a circular base of radius r=4. Find in each case the volume of the solid if all intersection between the solid and a plane perpendicular to a set diameter is:

a) A square

b) A triangle rectangle isosceles which one of its sides is on the circular base.

3. The attempt at a solution

The first I thought was in some kind of cylindroid. I know I must find an equation that I can integrate. So, the sides of the squares will be given by:

[tex]z=2\sqrt{r^2-x^2}[/tex]

Is the integration given by: [tex]\displaystyle\int_{-4}^{4}[2\sqrt{r^2-x^2}]^2dx=4\displaystyle\int_{-4}^{4}(r^2-x^2)dx[/tex] for the square?

And how can I find the volume of the other solid b)?

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# Homework Help: Intersection between the solid and a plane perpendicular

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