Please show step by step work. If you choose to do it on paper and upload a pict
ID: 2840413 • Letter: P
Question
Please show step by step work.
If you choose to do it on paper and upload a picture, please let it be legible.
A piece of wire 40 cm long is to be used to form the perimeters of a square and a circle in such a way as to make the total area a maximum. If the radius of the circle is r, then the circumference of the circle is 2 pi r. A length of 40 - 2 pi r is left for the four sides of the square. (2 pts.) The total area is A = .(3pts.)dA / dr = Find the value for r that will make the total area a maximum. What is the area of the square?Explanation / Answer
Area of circle =pi*r^2
lenghth of squate=(40-2*pi*r)/4
==> Area of square= (10-pi*r/2)^2
==> Total area= pi*r^2 +(10-pi*r/2)^2
==> dA/dr=2*pi*r -2*pi*(10-pi*r/2)/2=2*pi*r -pi*(10-pi*r/2)=(11.21r-31.4)
for area to be maximum dA/dr=0
==> (11.21r-31.4)=0
==> r=2.8011 cm
==> A=pi*2.8011^2+(10-pi*2.8011/2)^2=56 cm^2
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