A wire of length L can be used to make a circle and a square. How much of the wire should be used for each of the figures to maximise area?  

Expert Answers info

justaguide eNotes educator | Certified Educator

calendarEducator since 2010

write12,544 answers

starTop subjects are Math, Science, and Business

The total length of the wire is L. Let us use it to make a square of length x and a circle of radius r. The combined area of the shapes is x^2 + pi*r^2. The circumference of the square is 4x and that of the circle is 2*pi*r

4x + 2*pi*r = L

We have to maximize A = x^2 + pi*r^2

Differentiate L and A with respect to r

dA/ dr = 2*x(dx/dr) + 2*pi*r

dL / dr = 4(dx/ dr) + 2*pi

As L is a constant dL/dr = 0

=> 4(dx/ dr) + 2*pi = 0

=> dx / dr = -2*pi/4 = -pi/2

substitute in dA/dr

=> dA/ dr = 2*x(-pi/2) + 2*pi*r

=> dA/dr = -pi*x + 2*pi*r

Take the second...

(The entire section contains 2 answers and 347 words.)

Unlock This Answer Now


check Approved by eNotes Editorial

hala718 eNotes educator | Certified Educator

calendarEducator since 2008

write3,662 answers

starTop subjects are Math, Science, and Social Sciences

check Approved by eNotes Editorial