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# How many different-sized circles with positive integer radii have area

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Joined: 02 Sep 2009
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28 Nov 2017, 21:02
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45% (medium)

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68% (00:45) correct 32% (00:55) wrong based on 22 sessions

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How many different-sized circles with positive integer radii have areas less than 100?

(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen

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Re: How many different-sized circles with positive integer radii have area  [#permalink]

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28 Nov 2017, 21:29
B

For radius=6 the area is 113.09>100. Hence only upto 5

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29 Nov 2017, 16:13
1
Bunuel wrote:
How many different-sized circles with positive integer radii have areas less than 100?

(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen

I can see potential trouble with area = 100.

Area of circle is $$πr^2$$.

So it must be $$r^2 * 3.14 < 100$$, where r is an integer.

Radii 1, 2, 3, 4, and 5 (25 * 3.14 = approx 78) work.

Radius 6 does not: 36 * 3 = 108, so with 3.14 it would be higher.

Five values satisfy the conditions.

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Re: How many different-sized circles with positive integer radii have area  [#permalink]

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01 Dec 2017, 07:54
Bunuel wrote:
How many different-sized circles with positive integer radii have areas less than 100?

(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen

If r = 1, then the area of the circle is π(1)^2 = π.

If r = 2, then the area is π(2)^2 = 4π.

If r = 3, then the area is π(3)^2 = 9π.

If r = 4, then the area is π(4)^2 = 16π.

If r = 5, then the area is π(5)^2 = 25π.

Since π < 4, the area of any of the circles above will be less than 100. However, if r = 6, then the area of the circle will be π(6)^2 = 36π. However, since π > 3, 36π will be greater than 100. Thus, there are five different-sized circles with positive integer radii with area less than 100.

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Re: How many different-sized circles with positive integer radii have area &nbs [#permalink] 01 Dec 2017, 07:54
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