A level maths help needed!

A box is made from a square base of a side length x and height h. The surface area of the box (not including the lid) is 75cm2. Calculate the maximum volume of the box.

I've got that 4xh+x2=75 and that v=x2h but I'm not sure how to get any of the values

Reply 1

username5071070

v/h=x^2, and sub that into the first equation. just a guess, see where it gets you aha, good luck

(edited 4 years ago)

Reply 2

Juliakinga

Original post by katrinayates

v/h=x^2, and sub that into the first equation. just a guess, see where it gets you aha, good luck

why does v/h=x2?

Reply 3

vbzl

Original post by Juliakinga

From first eqt make h subject of formula then replace in second eqt. You will obtain V in terms of x. Differentiate V with respect to x and set to 0

Reply 4

Hilton184

Original post by Juliakinga

Both your equations are correct.

75=4xh+x^2

V=x^2 * h

We want to maximise the function V=x^2*h

Therefore, find V in terms of x only (i.e. rearrange your first equation for h, and then substitute it in to the volume equation).

Then you have a function for the volume in terms of x only. Now you can find the maximum by differentiating and setting equal to 0 (maximum is stationary points).

This problem is quite similar to one I made a video on a few days ago - its another problem where you need to find the maximum of something, in a problem which is in context and thus more difficult than your average differantiation problem. It's worth having a look at! Let me know if you find it interesting and if you manage to get it! [Link to another similar problem].

Reply 5

Juliakinga

Original post by Hilton184

So when I differentiate and get the equation 75/4 - 3/4 x^2, what do I get when I solve the equation. Is this the length x?

Reply 6

vbzl

Original post by Juliakinga

So when I differentiate and get the equation 75/4 - 3/4 x^2, what do I get when I solve the equation. Is this the length x?

Yes it is the length that will give you max Volume.

Reply 7

Muttley79

Original post by Juliakinga

So when I differentiate and get the equation 75/4 - 3/4 x^2, what do I get when I solve the equation. Is this the length x?

I can't see an equation, just an expression ... yes, when it is an equation it will give you x. You then need to find the volume.

Reply 8

Hilton184

Original post by Juliakinga

So when I differentiate and get the equation 75/4 - 3/4 x^2, what do I get when I solve the equation. Is this the length x?

Yes, that is correct when you differentiate. You get dV/dx = 75/4 -3/4 (x^2).

Now, if you set this equal to 0 and solve for x, you will obtain the x value which gives the maximum volume. This is because dV/dx is the gradient function and when it is equal to 0 it is a stationary point (maximum point in this case). If you watch the video I linked this does a similar problem but demonstrates how the maximum is obtained when you differentiate a function like this. Hope this helps!