C2 - applications of differentiation Watch

Poshtotty
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#1
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An open rectangular box is to be made with an external area of 1620 cm^2.

Ratio of the lengths of the sides of the base of the box is 3:5.

Height is h cm.

The length of shorter side is 3x cm.


I have managed to work out that the length of the longer side is 5x cm, the volume is 15hx^2, and the external area is (16xh + 15x^2) cm^2. I have checked and it is all correct.

However, I am asked to show that h = (1620 - 15x^2) / 16x

I am not sure how to do this.
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Rocious
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External area = 16xh + 15x^2 = 1620

And then you can jammy it about to isolate h.
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Poshtotty
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(Original post by Rocious)
External area = 16xh + 15x^2 = 1620

And then you can jammy it about to isolate h.
Oh right. I can't believe I didn't think of that. Thank you.
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Poshtotty
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(Original post by Rocious)
External area = 16xh + 15x^2 = 1620

And then you can jammy it about to isolate h.
Any idea how I would work out V in terms of x?

For V, I have 15hx^2.

I would think that V = Area x height.

But when I multiply those values and rearrange, I don't get the answer given which is:

V = 15/16x (1620 - 15x^2)
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Rocious
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Should that be 15/16 and not 15/6?

Anyways,

V = 15hx^2

and h = (1620 - 15x^2) / 16x
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