Carcass wrote:
Square ABCD has a side of 20. Circle O has a radius of r. If the circle has MORE AREA than does the square, then which of the following could be the value of r?
Indicate all possible values of the radius.
A. 8
B. 9
C. 10
D. 11
E. 12
F. 13
G. 14
H. 15
Area of square = side² = 20² =
400Let's first determine how big the radius needs to be in order for the circle's area to
EQUAL the square's area (of
400).
Area of circle \(= \pi r^2\)
So we want: \(\pi r^2 = 400\)
Divide both sides of the equation by \(\pi\) to get: \(r^2 = \frac{400}{\pi}≈\frac{400}{3.14}≈127.4\)
Take the square root of both sides to get: \(r ≈ \sqrt{127.4}≈11.3\)
So, when the radius of the circle is approximately 11.3, the area of the circle EQUALS the area of the square.
So if the circle's radius is
greater than 11.3, the area of the circle will be greater than the area of the square
Answer choices E, F, G, and H are all greater than 11.3
Answer: E, F, G, and H
Cheers,
Brent