Question

A thin piece of wire 40 metres long is cut into two pieces. One piece is used to form a circle with radius r , and the other is used to form square. No wire if left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r? 

A) πr^2
B) πr^2 + 10
C) πr^2 + ¼(πr)^2
D) πr^2 + (40 - 2πr)^2
E) πr^2 + (10 - ½πr)^2

Answer 1

The circumference of Circle =>  a  = 2πr
The perimeter length of Squre => 40 - a
length of a side = (40 - a) / 4 => 10 - (a/4)
Total Area  = Total Area of Circle  + total area of square
=> πr^2 + (10 - (a/4))^2 // since a = 2πr, replace we get
=> πr^2 + (10 - ½πr)^2
Hence answe is E