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AleksandrR [38]
3 years ago
11

HELP ME IM GONNA LOSE MY MIND IN MINUTES

Mathematics
2 answers:
VLD [36.1K]3 years ago
7 0
Oh gosh that’s hard try using a calculator if you can
Nonamiya [84]3 years ago
5 0

Answer:

I already lost my mind use a calculator that all I got for you sorry

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A container manufacturing company was contracted to design and manufacture cylindrical cans for fruit juice. The volume of each
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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}})}}

The given parameter is:

\mathbf{V = 0.946}

The volume of a cylinder is calculated as:

\mathbf{V = \pi r^2 h}

Make h the subject

\mathbf{h = \frac{V}{ \pi r^2}}

The surface area (A) of a cylinder is:

\mathbf{A = \pi r^2 + \pi rh}

Substitute \mathbf{h = \frac{V}{ \pi r^2}}

\mathbf{A = \pi r^2 + \pi r \times \frac{V}{\pi r^2}}

\mathbf{A = \pi r^2 + \frac{V}{r}}

Differentiate

\mathbf{A' = 2\pi r - Vr^{-2}}

Set to 0

\mathbf{2\pi r - Vr^{-2} = 0}

Rewrite as:

\mathbf{ 2\pi r = Vr^{-2}}

Multiply through by r^2

\mathbf{ 2\pi r^3 = V}

Solve for r

\mathbf{r = \sqrt[3]{\frac{V}{2\pi}}}

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So, we have:

\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}

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}})}}

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