Problem Solving

Hey all,

Couldn't figure this one out. A brief explanation would be much appreciated. Thanks!

68) A thin piece of 40 m wire is cut in two. One piece is a circle with radius of r. Other is a square. No wire is left over. Which represents total area of circle and square in terms of r?

a. Πr^2
b. Πr^2 + 10
c. Πr^2 + ¼ π^2r^2
d. Πr^2 + (40 - 2πr)^2
e. Πr^2 + (10 - ½ Πr)^2

(FYI, those are pis above)

PKW-
Can you please post the answers when you are posting all of these questions?

The amount of wire used for the circle is 2ÃŽr
The amount of wire left for the square is (40 - 2ÃŽr)
The area of the circle is ÃŽr^2

So the total area is represented by:
ÃŽr^2 (Total Area of the Circle) + (40 - 2ÃŽr)^2 (Total Perimeter of the Square)

In order to find the area of the square you must find the length of one of the sides and square it.
(40 - 2ÃŽr)/4. You must divide this by 4 because it represents the total perimeter of all 4 sides and you need the length of just one side.

Answer is Îr^2 (Total Area of the Circle) + (10 - ½ Î r)^2 (area of the square)

Yes, I will be sure to post the answers in the future. FYI, you were correct

1) how come you didn't divide the wire into 2 equal parts to begin with? in other words, how come you didn't say 2 pi r = 20, solve for r and then plug that into pi r ^2?

thanks again!

the question doesnt mention that the wire was cut into 2 equal halves. Hence we need to consider the circumference of the circle (since radius r is given) and subtract it from the total length to get the perimeter of the square.
Using the perimeter of the square, we can calculate the area of the square. Since we know the radius of the circle we can calculate the area of the circle.

Hope it helps

Thanks, gmatv! Have to always remember to read the question stem carefully.