Please provide the editorial of question The Best Box

Letâ€™s understand this question in a different way

Johnny needs to make a rectangular box for his physics class project, Letâ€™s understand it into different wayâ€¦ His teacher slapped him and told â€¦ â€śGo to your home, and make project for me to find the largest volume of the box that you could makeâ€¦â€ť

Johny asked â€śHow can i do that madam?â€ť

Madam: You have to make a **rectangular box**. Youâ€™ve given **P cm** of wire and **S cm2** of special paperâ€¦ (Hope so johnny, you know this is an **area of paper**). Youâ€™d have to use all those wire to make **12 edges**.

Johnny: 12 edges? I donâ€™t understand madam?..

Madam: **SLAPPED!!** â€¦ Foolâ€¦ look at this pictureâ€¦

Johnny: Okay madamâ€¦ Please continueâ€¦

Madam: And paper for six sidesâ€¦

Johnny: And what is this madam?

Madam: **Again SLAPPED!!..** Look at this pictureâ€¦

Johnny: got itâ€¦ please continueâ€¦

Madam: Now, youâ€™ve to find the largest **volume of the Box**.

Madam: Do you know **volume of box mean**?

Madam: Itâ€™s okay â€¦ look at this picâ€¦

HOPE YOU FIND THE BEST ANSWER!!..

This problem is purely based on mathematics,just brush up your concepts of maxima and minima and then try to derive a formula. Hope it helps!

The volume V=l*b*h

Now using 4(l+b+h)=P and 2(lb+bh+hl)=S

Convert the above formula of V in terms of only h so that we can differentiate it and then get the value of h for where the volume will maximize or minimize.

If you make the right subsitutions the volume will come out to be equal to (S/2-h(P/4-h))*h.

Differentiate the above and then you will get two values of h. One will be for maximum value and other will be for minimum value. Use a if statement to find out which one is which.

Also use double which will have better precision.

Hope this helps:).