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The circle above has area 25.

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The circle above has area 25. [#permalink] New post 20 Sep 2018, 16:35
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Question Stats:

60% (00:39) correct 40% (00:21) wrong based on 10 sessions
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The circle above has area 25.

Quantity A
Quantity B
The length of chord AB
\(10\)


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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Re: The circle above has area 25. [#permalink] New post 21 Sep 2018, 07:04
Expert's post
sandy wrote:
Attachment:
Capture.JPG


The circle above has area 25.

Quantity A
Quantity B
The length of chord AB
\(10\)


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.


Area of circle = πr² (where r = radius)

So, we can write: πr² = 25
Approximate π to write: 3r² ≈ 25 [yes, we often use 3.14 as the approximation for π, but you'll see why 3 works just as well]
Divide both sides by 3 to get: r² ≈ 25/3
Simplify: r² ≈ 8.3333...
So, r ≈ √8.33333

Since √9 = 3, we know that √8.33333 is less than 3
This means the radius is less than 3, which means the DIAMETER is less than 6
So, the greatest possible length of chord AB is still less than 6

We get:
Quantity A: some number less than 6
Quantity B: 10

Answer: B

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Re: The circle above has area 25.   [#permalink] 21 Sep 2018, 07:04
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The circle above has area 25.

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