Please answer the question above thank you. A piece of wire of length 55 is cut,
ID: 2828257 • Letter: P
Question
Please answer the question above thank you.
A piece of wire of length 55 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square? (a) To minimize the combined area, the wire should be cut so that are used for the circle and are used for the square. Type integers or decimals rounded to the nearest thousandth as needed.) (b) To maximize the combined area, the wire should be cut so that are used for the circle and are used for the square Type integers or decimals rounded to the nearest thousandth as needed.)Explanation / Answer
let circle be made of x and square be made by 55-x
so 2.pi.r = x and 4a = 55-x (perimeters)
r= x/2pi and a = 55-x/4
Combined area is pir^2 + (55-x/4)^2
A(x) = x^2/4pi + (55-x)^2 / 16
A'(x) = x/2pi - (55-x)/8 i.e x = 24.1945 For minimum area
For maximum area let the entire wire be used to make a circle.