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If the circumference of a circle is less than [m]16\pi[/m],
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01 Apr 2020, 09:32
01 Apr 2020, 09:32
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If the circumference of a circle is less than \(16\pi\), which of the following could be the area of the circle?
A. \(49\pi\)
B. \(64\pi\)
C. \(81\pi\)
D. \(101\pi\)
E. \(256\pi\)
Kudos for the right answer and explanation
A. \(49\pi\)
B. \(64\pi\)
C. \(81\pi\)
D. \(101\pi\)
E. \(256\pi\)
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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Re: If the circumference of a circle is less than [m]16\pi[/m],
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01 Apr 2020, 09:47
01 Apr 2020, 09:47
Carcass wrote:
If the circumference of a circle is less than \(16\pi\), which of the following could be the area of the circle?
A. \(49\pi\)
B. \(64\pi\)
C. \(81\pi\)
D. \(101\pi\)
E. \(256\pi\)
Kudos for the right answer and explanation
A. \(49\pi\)
B. \(64\pi\)
C. \(81\pi\)
D. \(101\pi\)
E. \(256\pi\)
Kudos for the right answer and explanation
Circumference of circle \(=2\pi r\)
So we can write: \(2\pi r<16\pi\)
Divide both sides of the inequality by \(2\pi\) to get: \(r<8\)
In other words, the radius is less than 8
Area of circle \(=\pi r^2\)
If the radius were EQUAL to \(8\), then the area of the circle \(=\pi (8^2)=64\pi\)
Since the radius is less than 8, the area of the circle must be LESS THAN \(64\pi\)
Answer choice A is the only answer that is less than \(64\pi\)
Answer: A
Cheers,
Brent
gmatclubot
Re: If the circumference of a circle is less than [m]16\pi[/m], [#permalink]
01 Apr 2020, 09:47
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