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# A circle with radius

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Founder
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A circle with radius [#permalink]  19 Oct 2017, 14:56
Expert's post
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Question Stats:

94% (00:37) correct 5% (01:01) wrong based on 38 sessions

A circle with radius $$\frac{4}{\sqrt{\pi}}$$ has the same area as a particular square.

 Quantity A Quantity B $$9\pi$$ The area of the square if each side were increased by 1

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Intern
Joined: 23 Sep 2017
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Re: A circle with radius [#permalink]  21 Oct 2017, 04:10
Please explain how choice a is correct? n is not known in this question.
Founder
Joined: 18 Apr 2015
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Kudos [?]: 2052 [1] , given: 8116

Re: A circle with radius [#permalink]  22 Oct 2017, 14:42
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Expert's post
The circle with radius $$\frac{4}{\sqrt{n}}$$ is equal to the area of a square.

Use the circle area formula

$$A = \pi ( \frac{4}{\sqrt{n}}) ^2$$

A = 16

Hence the area of the square is 16 and a single side is 4.

Now QB says if the side is increased by one. Therefore, one side is 5. From this the area is 25.

But QA is $$9 \pi$$ that is more than 27 ( 9 * 3.14).

The answer is A
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Intern
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Kudos [?]: 7 [1] , given: 6

Re: A circle with radius [#permalink]  22 Oct 2017, 22:41
1
KUDOS
Carcass wrote:
The circle with radius $$\frac{4}{\sqrt{n}}$$ is equal to the area of a square.

Use the circle area formula

$$A = \pi ( \frac{4}{\sqrt{n}}) ^2$$

A = 16

Hence the area of the square is 16 and a single side is 4.

Now QB says if the side is increased by one. Therefore, one side is 5. From this the area is 25.

But QA is $$9 \pi$$ that is more than 27 ( 9 * 3.14).

The answer is A

Hi Carcass,

Thanks.

Denominator is \sqrt{n}, not pi. Please change the question.
Director
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Re: A circle with radius [#permalink]  23 Oct 2017, 02:05
2
KUDOS
AR15J wrote:
Carcass wrote:
The circle with radius $$\frac{4}{\sqrt{n}}$$ is equal to the area of a square.

Use the circle area formula

$$A = \pi ( \frac{4}{\sqrt{n}}) ^2$$

A = 16

Hence the area of the square is 16 and a single side is 4.

Now QB says if the side is increased by one. Therefore, one side is 5. From this the area is 25.

But QA is $$9 \pi$$ that is more than 27 ( 9 * 3.14).

The answer is A

Hi Carcass,

Thanks.

Denominator is \sqrt{n}, not pi. Please change the question.

Question edited consistently with the source
Re: A circle with radius   [#permalink] 23 Oct 2017, 02:05
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# A circle with radius

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