Unable to find the base

[Abhishekdas]

How do I find the base length in terms of x or y?

 

[MarkFL]

I would write the lenght of the leg in terms of \(\displaystyle y\), presuming we are computing the volume of the solid being described, since the thickness of each slice will be \(\displaystyle dy\). The length of the base is \(\displaystyle 2x\) where \(\displaystyle 0\le x\) and we know:

\(\displaystyle 2x=2\sqrt{1-y^2}\)

And so the volume of an arbitrary slice is

\(\displaystyle dV=\frac{1}{2}\left(2\sqrt{1-y^2}\right)^2\,dy=2\left(1-y^2\right)\,dy\)

Using even symmetry, I would then write:

\(\displaystyle \displaystyle V=4\int_0^1 \left(1-y^2\right)\,dy=\,?\)

 

[Abhishekdas]

I would write the lenght of the leg in terms of \(\displaystyle y\), presuming we are computing the volume of the solid being described, since the thickness of each slice will be \(\displaystyle dy\). The length of the base is \(\displaystyle 2x\) where \(\displaystyle 0\le x\) and we know:

\(\displaystyle 2x=2\sqrt{1-y^2}\)

And so the volume of an arbitrary slice is

\(\displaystyle dV=\frac{1}{2}\left(2\sqrt{1-y^2}\right)^2\,dy=2\left(1-y^2\right)\,dy\)

Using even symmetry, I would then write:

\(\displaystyle \displaystyle V=4\int_0^1 \left(1-y^2\right)\,dy=\,?\)

Yeah! That makes sense. I found out the answer to be 8/3.

 

[Denis]

Were you able to solve this one you posted 4 years ago:
https://www.freemathhelp.com/forum/threads/86448-Please-help?p=355205#post355205