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

Indicate all possible values of the radius.

A. 8

B. 9

C. 10

D. 11

E. 12

F. 13

G. 14

H. 15

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Official Answer

E,F,G,H

Retired Moderator

Joined: **10 Apr 2015 **

Posts: **6218**

Given Kudos: **136 **

Re: Square ABCD has a side of 20. Circle O has a radius of r. If
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26 Apr 2020, 16:46

2

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

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

Re: Square ABCD has a side of 20. Circle O has a radius of r. If
[#permalink]
14 Jun 2020, 03:13

1

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

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

Re: Square ABCD has a side of 20. Circle O has a radius of r. If
[#permalink]
19 Jul 2020, 04:28

1

Given circle with radius R has area bigger than Square with side 20

Asking what COULD be the value of R?

Area of that square is (20)^2=400

Now the area of circle MUST be greater that 400.

and by testing each choice we can see that E F G H meet that condition.

Asking what COULD be the value of R?

Area of that square is (20)^2=400

Now the area of circle MUST be greater that 400.

and by testing each choice we can see that E F G H meet that condition.

gmatclubot

Re: Square ABCD has a side of 20. Circle O has a radius of r. If [#permalink]

19 Jul 2020, 04:28
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