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**The hoop has radius R.**

I used the same way to plot the axis for the hoop:

##l^2 = r^2= 4R^2cos\theta##

since:

I used the same way to plot the axis for the hoop:

##l^2 = r^2= 4R^2cos\theta##

since:

**##**r=2Rcos\theta##**2\rho \int_{0}^{\frac{\pi}{2}} r^2 r d\theta****[tex]**

answer is

using the same method to find mass is also wrong, which suggest a fundamental mistake in my solution but I don't know what it is.

**2\rho \int_{0}^{\frac{\pi}{2}} 8**

[tex]**[/tex]**[tex]

**R^3 cos^3\theta**d\theta**[/tex]**answer is

**\frac{32}{3}R^3\rho****[tex]****, and its wrong****[/tex]**using the same method to find mass is also wrong, which suggest a fundamental mistake in my solution but I don't know what it is.

**2\rho \int_{0}^{\frac{\pi}{2}} r d\theta****[tex]**

that's equal**2\rho \int_{0}^{\frac{\pi}{2}} 2**

[tex]**[/tex]**[tex]

**R cos\theta**d\theta**[/tex]**that's equal

**4\pi r****[tex]****which is wrong****[/tex]****what is wrong with my solution?, it was really bizarre when I found that the mass itself using the limits I found actually gives a wrong answer.**

What did I miss?

What did I miss?

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