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Square ABCD has a side of 20. Circle O has a radius of r. If

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Square ABCD has a side of 20. Circle O has a radius of r. If [#permalink] New post 30 Nov 2018, 16:59
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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
[Reveal] Spoiler: OA

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Re: Square ABCD has a side of 20. Circle O has a radius of r. If [#permalink] New post 26 Apr 2020, 16:46
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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 = 400

Let'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
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Re: Square ABCD has a side of 20. Circle O has a radius of r. If [#permalink] New post 14 Jun 2020, 03:13
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Area of Circle: pi*r^2
Area of square = side * side = 20 * 20 = 400
area of circle > area of square
pi*r^2>400

now check the values, starting from last
3.142*15^2>400
706.95>400

Similarly check values till 12. The value on 12 is around 402 so this automatically means rest of others must be less than 400
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Re: Square ABCD has a side of 20. Circle O has a radius of r. If   [#permalink] 14 Jun 2020, 03:13
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