MaXimUm/MiniMuM QuestiOn (1 Viewer)

[+GriM ReApeR+]

A window consists of a rectangle surmounted by a semicircle having as its diameter the width of the rectangele. If the perimeter of window is 10m find the radius of the semicircle which will give the greatest possible area for the window.

The answer is supposed to be 1.4m(approx) but I keep on getting the wrong answer...pls help...

 

[Xayma]

Let width=x
Let Height=y

P=x+2y+1/2*pi*x
10=x+2y+1/2*pi*x
y=[10-x(1+1/2*pi)]/2

A=xy+1/2*pi*x²/4
A=xy+1/8*pi*x²
Sub the y from above in, do the standard derivative, do concavity, then the radius= 1/2 x

 

[+GriM ReApeR+]

Originally posted by Xayma
Let width=x
Let Height=y

P=x+2y+1/2*pi*x
10=x+2y+1/2*pi*x
y=[10-x(1+1/2*pi)]/2

A=xy+1/2*pi*x²/4
A=xy+1/8*pi*x²
Sub the y from above in, do the standard derivative, do concavity, then the radius= 1/2 x

yea I got that....but somehow I stuffed it up. Thanks anyway, at least I know that my working out is correct