A piece of wire 20 cm long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. Atwhat length should the wire be cut to minimize the total area enclosed?...
A piece of wire 20 cm long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. At
what length should the wire be cut to minimize the total area enclosed?
kindly help me in solving this problem?
The pieces of wire should be 11.20cm (2 d. p.) and 8.80cm (2 d. p).
thank you so very much...............
Let length of one piece of wire be x, which bent into circle.
Thus circumference of cirle be x. Let radius of the circle be r, so
Thus area of the circle be
Perimeter of the square be
Thus side of the square be (20-x)/4
Thus area of the square be
Total enclosed area be
For maximum / minimum, we have
Thus pieces of wire should be 11.202 cm. and 8.798 cm.