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C1 applications of diffrentiation question help

"A cuboid has a volume of 8m3 . The base of the cuboid is square with sides of length x metres. The surface area of the cuboid is A m3 .
Show that A=2x2 +32/x"

I know that the volume of a cuboid is Length x Width x Height

But I don't know how to find the sides of the cuboid. Is it 2(lw+wh+hl)? I don't really think it is. Even of it was how did we get a fraction with x in the denominator?
As you say the volume is x^2h=8

So h=8/x^2

You know the area of the base and the top are both x^2 so that is where the 2x^2 comes from

Now you know h so what is the area of each side ... You will have 4 of these
Original post by Fruitbasket786
"A cuboid has a volume of 8m3 . The base of the cuboid is square with sides of length x metres. The surface area of the cuboid is A m3 .
Show that A=2x2 +32/x"

I know that the volume of a cuboid is Length x Width x Height

But I don't know how to find the sides of the cuboid. Is it 2(lw+wh+hl)? I don't really think it is. Even of it was how did we get a fraction with x in the denominator?

w = d = x

v = hx2
8 = hx2

surface area = 2(hx + hx + x2)
A = 2x2 + 4hx

See if you can find where to go from there.
Original post by TenOfThem
As you say the volume is x^2h=8

So h=8/x^2

You know the area of the base and the top are both x^2 so that is where the 2x^2 comes from

Now you know h so what is the area of each side ... You will have 4 of these


I can see what's going on, thanks! I'll try to do the other parts of the question and see how it goes.

Edit: I noticed that you got the denominator as x^2 when the denominator is supposed to be just x to the power of one.
(edited 9 years ago)
Original post by Fruitbasket786
I can see what's going on, thanks! I'll try to do the other parts of the question and see how it goes.

Edit: I noticed that you got the denominator as x^2 when the denominator is supposed to be just x to the power of one.


That is the denominator of h

You are trying to find the areas of the faces
Original post by TenOfThem
That is the denominator of h

You are trying to find the areas of the faces

I know that the height of it is 8/x^2 and that you multiply it by four to get 32/x^2
But the question says to show that A=2x2 +32/x so what's up with that?
Original post by Fruitbasket786
I know that the height of it is 8/x^2 and that you multiply it by four to get 32/x^2
But the question says to show that A=2x2 +32/x so what's up with that?

The cuboid has six sides. Four of these will add to 32/x and the end sides will be squares of side x.

this totals to A = 2x2​ + 32/x
Original post by Fruitbasket786
I know that the height of it is 8/x^2 and that you multiply it by four to get 32/x^2
But the question says to show that A=2x2 +32/x so what's up with that?


You are looking for the surface area

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