V = 4/3πr^3V = 4/3 (π) (6.5)^3
V = 366.1666π (6 repeat)
answer is 366.16 π (3rd choice)
Yes, because if it has brackets, it just means it is an absolute value
The volume of the cylinder is the amount of fruit juice it can contain.
The relationship between the volume and the surface area is:
![\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%20%3D%20%5Cpi%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%29%5E2%20%2B%20%5Cfrac%7B0.946%7D%7B%28%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%29%7D%7D)
The given parameter is:

The volume of a cylinder is calculated as:

Make h the subject

The surface area (A) of a cylinder is:

Substitute 


Differentiate

Set to 0

Rewrite as:

Multiply through by r^2

Solve for r
![\mathbf{r = \sqrt[3]{\frac{V}{2\pi}}}](https://tex.z-dn.net/?f=%5Cmathbf%7Br%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%7D)

So, we have:
![\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%20%3D%20%5Cpi%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%29%5E2%20%2B%20%5Cfrac%7B0.946%7D%7B%28%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%29%7D%7D)
Hence, the relationship between the volume and the surface area is:
![\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%20%3D%20%5Cpi%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%29%5E2%20%2B%20%5Cfrac%7B0.946%7D%7B%28%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%29%7D%7D)
Read more about surface areas and volumes at:
brainly.com/question/3628550