Maths

A fish tank in the shape of a cuboid is to be made from 1600 cm^2 of glass.
The fish tank will have a square base of side length x cm, and no lid. No glass is wasted. The glass can be assumed to be very thin.
(a) Show that the volume, V cm , of the fish tank is given by V = 400x -x^3/4
(b) Given that x can vary, use differentiation to find the maximum or minimum value of V.
(c) Justify that the value of V you found in part b is a maximum.

Need help with all of it, I haven't started the first part as I don't know how to start. Some help with this will be appreciated, thanks in advance.

For the first part, work out the area of the base and hence the sides (remaining area) which gives the height and the volume is the product of the base area with the height.

Could you possibly give a bit more help, how would I do that. What values do I use, any steps I should follow? please and thank you

Not really. The first part is pretty much gcse and similar to drawing a net, though the info about material not being wasted is important. Why not sketch it out and upload what you think for the
* base area
* total - base area
* height of sides

Well the base side lengths are xcm. Total surface area is 1600cm^2. I would guess you would do problem solving and do
1600-x2
and then divide 4x to get the height of the sides?

and ...

put it into the equation?

The volume is ...
Thats what the question asks for.

400x - x^3/4?

The question tells you its correct.

How would I do part B?

The question says use differentiation to ... What are you stuck with?

I have differentiated and got 400 - 3/4x^2
Is there anything I do further to get the min or max value?

Do you have a textbook? It would be fully covered in there as finding min/max/stationary points is a key topic.

Yes I do. I'll give it a look rn.. I Actually have my AS mock exams in 2 weeks and I procrastinated the whole year. And now I'm actually revising when it's too late. This question is in a practice paper that I'm going through rn.

Sure, but you have to get the key understanding in place and test it on questions such as these.
If you're too focussed on working though model solutions, you may (will) find it difficult to generalize/apply to similar questions.
A good habit of getting into when you post questions like these is to force yourself into posting some working, even if its wrong. That way you try and formulate the approach/ideas, rather than just running through the numbers/algebra.

I see. Noted, thanks.

I see it now, I have to let the differentiation equal to 0 and then solve the equation to find x, then sub it into the original value.

Of course. Stationary points are when
grad = 0
and these could be min/max/inflection. Then c) asks you to reason about their nature. Again, look in your textbook and post some ideas/... if youre still

The Question says to justify the value of v in part b is the maximum. I got 6332 as my answer in b. So do I just state,
V= 6332
6332 > 0 hence the value is a maximum of V.