One approach is to plug in a value for r and see what the output should be.A thin piece of 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 the square regions in term of r?
A)(pi)r²
B)(pi)r² + 10
C)(pi)r² + 1/4([pi]² * r²)
D)(pi)r² + (40 - 2[pi] * r)²
E)(pi)r² + (10 - 1/2[pi] * r)²
Let's say r = 0. That is, the radius of the circle = 0
This means, we use the entire 40-meter length of wire to create the square.
So, the 4 sides of this square will have length 10, which means the area = 100
So, when r = 0, the total area = 100
We'll now plug r = 0 into the 5 answer choices and see which one yields an output of 100
A) (pi)(0²) = 0 NOPE
B) (pi)(0²) + 10 = 10 NOPE
C) (pi)(0²) + 1/4([pi]² * 0²) = 0 NOPE
D) (pi)(0²) + (40 - 2[pi]0)² = 1600 NOPE
E) (pi)(0²) + (10 - 1/2[pi](0))² = 100 PERFECT!
Answer: E
Cheers,
Brent
