Let A be the total surface area of a rectangular container of square base and height, h. At a certain instant, the surface area is decreasing at 24 cm^2/s while the width of the base is 5 cm and increasing at 2 cm/s. Determine whether the height is increasing or decreasing at that instant if the height is 3 cm. (Ans: dh/dt = -4.4 cm/s)
Somebody PLEAAAAAASSSEEE explain this to me. :(

Question

Let A be the total surface area of a rectangular container of square base and height, h. At a certain instant, the surface area is decreasing at 24 cm^2/s while the width of the base is 5 cm and increasing at 2 cm/s. Determine whether the height is increasing or decreasing at that instant if the height is 3 cm. (Ans: dh/dt = -4.4 cm/s)
Somebody PLEAAAAAASSSEEE explain this to me. :(

radar · Answer

This appears to be a related rate problem, but the answer tells you that the height is decreasing (note the - in the -4.4cm/sec.

anonymous · Answer

okay :/ how do i solve it?

radar · Answer

Where did the answer come from?  If that is your answer, then you have already solved it.

anonymous · Answer

got it from the lecturer. but i have no idea how to solve it.

radar · Answer

O.K. First you need to express the total surface area (A) in terms of the base and height.
The base is square (given) so assign x as the dimension of the base.  The surface area of the base is then x^2 (x squared).  This is not the total A, just the base area.

The area of the rest of the container is to be expressed in terms of x (base dimension) and h (height).  There are 4 sides each having an area hx, so that equals 4hx.  Now the total surface area A is:$$x ^{2}+4hx$$.  You must understand this before proceeding.  Do you?

anonymous · Answer

okay. go on.

anonymous · Answer

so the top of the rectangle doesnt count?

radar · Answer

Do you understand rate of change or derivatives?  No it is a container, no mention of a lid, but if it did count the terms which is now x^2 would become 2x^2.  we can work it both ways, because it might be a closed container.

anonymous · Answer

okay i understand. so then we find dA/dh? and the x remains? after that what?

radar · Answer

A'=-24 (cm)^2   given
You are also given x' as 2cm/s
you are given x (x = 5) 
you are given h (h=5)
solve for h'

radar · Answer

I am kind of rusty here on implicit differentiation, hopefully you are current.

radar · Answer

*h=3

radar · Answer

I come up with -3.666 not the approved answer.  I will try with the lid!

anonymous · Answer

thank you so much! appreciate your help :)

radar · Answer

With the lid I get -5.55   somewhere I've erred, suggest going over it or did you get the -4.4

anonymous · Answer

no i didnt get it :/