she would need 166 boxes. there is a remainder of 1. one book wont fit in a box
G, the y-intercept will not be 3
Answer:
<em>r=3x</em>
Step-by-step explanation:
<u>The Volume of a Cone</u>
The volume of a cone of radius r and height h is:
![\displaystyle V=\frac{1}{3}\pi hr^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20hr%5E2)
We are given the volume of a cone is
![V=3\pi x^3](https://tex.z-dn.net/?f=V%3D3%5Cpi%20x%5E3)
Equating:
![\displaystyle \frac{1}{3}\pi hr^2=3\pi x^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20hr%5E2%3D3%5Cpi%20x%5E3)
Multiplying by 3:
![\pi hr^2=9\pi x^3](https://tex.z-dn.net/?f=%5Cpi%20hr%5E2%3D9%5Cpi%20x%5E3)
Simplifying by pi:
![hr^2=9 x^3](https://tex.z-dn.net/?f=hr%5E2%3D9%20x%5E3)
Since h=x:
![xr^2=9 x^3](https://tex.z-dn.net/?f=xr%5E2%3D9%20x%5E3)
Dividing by x:
![r^2=9 x^2](https://tex.z-dn.net/?f=r%5E2%3D9%20x%5E2)
Taking square roots:
![r=\sqrt{9 x^2}=3x](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B9%20x%5E2%7D%3D3x)
Thus: r=3x