Problem Solving

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

1) πr^2
2) πr^2 + 10
3) πr^2 + 1/4π^2r^2
4) πr^2 + (40 - 2πr)^2
5) πr^2 + (10 - 1/2πr)^2

the answer is 5

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

1) πr^2
2) πr^2 + 10
3) πr^2 + 1/4π^2r^2
4) πr^2 + (40 - 2πr)^2
5) πr^2 + (10 - 1/2πr)^2

the answer is 5

Area of the circle = πr^2

Area of the square = one of it's sides squared

Perimeter of the square is 40 - (the perimeter of the circle = 2Ï€r)

One of the sides of the square = 40-2Ï€r/4 or 10-1/2Ï€r

Total area: πr^2 + (10-1/2πr)^2

JeffB wrote:

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

1) πr^2
2) πr^2 + 10
3) πr^2 + 1/4π^2r^2
4) πr^2 + (40 - 2πr)^2
5) πr^2 + (10 - 1/2πr)^2

the answer is 5

Area of the circle = πr^2

Area of the square = one of it's sides squared

Perimeter of the square is 40 - (the perimeter of the circle = 2Ï€r)

One of the sides of the square = 40-2Ï€r/4 or 10-1/2Ï€r

Total area: πr^2 + (10-1/2πr)^2

correct.