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3 years ago

Please help me. I will give you brainliest!

Mathematics

2 answers:

MrMuchimi3 years ago

6 0

Answer:

50 6 300

10 2 20

Step-by-step explanation:

pls i need brainleest i need it to level up again

Dvinal [7]3 years ago

3 0

Answer:

50 6 300

10 2 20

Step-by-step explanation:

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

gtnhenbr [62]

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

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

$\mathbf{A = \pi r^2 + \frac{0.946}{r}}$

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:

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

Read more about surface areas and volumes at:

brainly.com/question/3628550

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2 years ago

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