Max Min problem, HELP!!! (1 Viewer)

[RHINO7]

A rectangle is cut from a cylinder disc of radius 6cm. Find the area of the largest rectangle that can be produced.

 

[nathan71088]

This is a very sneaky question. I am not sure how to create a diagram to answer it. The way to go ahead is to draw the disc and then inside draw the rectangle with its corners touching the disc. Draw the diameter to be touching two opposite (non-adjacent sides). Work from here but if you still have problems ill try to find a way to draw the diagram.

 

[pLuvia]

First find the circumference of your cylinder disc, then let the sides of the rectangle be x and y

Total perimeter
2x+2y=2*6*pi
x+y=6pi

Area
A=xy

Now make x or y the subject from the perimeter
i.e. if y were the subject: y=6pi-x
A=x(6pi-x)
A'=6pi-2x
A"=-2

Now find the turning point using A', and from observation that point will be a maximum since A''<0

Now then you say: The rectangle is a maximum when x=blah blah

Then simply find the other side, y, and then multiply both together to get the maximum area

Just from observation of the question, you should find that the x and y values are the same, since the largest area a rectangle could have is if it is a square

Answer should be 9pi² cm²