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The circumference of Circle A is twice the circumference of

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The circumference of Circle A is twice the circumference of [#permalink] New post   19 Oct 2017, 14:47
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The circumference of Circle A is twice the circumference of Circle B

Quantity A
Quantity B
The area of Circle A
Twice the area of Circle B


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.
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A
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IlCreatore
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Re: The circumference of Circle A is twice the circumference of [#permalink] New post   20 Oct 2017, 06:50
The information about the circumferences can be translated into \(C_a = 2\pi r_a = 2C_b = 2*2\pi r_b\).

Then, the area of circle A becomes \(A_a = \pi r_a^2 = 2\pi r_b^2\), while the area of circle B is \(A_b = \pi r_b^2\).

Simplifying we get quantity A equal to 2 and quantity B equal to 1.

Answer A
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Re: The circumference of Circle A is twice the circumference of [#permalink] New post   02 Nov 2020, 04:31
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Cricumference of A = 2 * Pi * rA = 2 ( 2 * Pi * rB) = 4 * Pi rB

=> 2 * Pi * rA = 4 * Pi * rB we factorize and get rA = 2 rB

Area of A = Pi * rA^2 = Pi * [(2rB)^2] = Pi * 4 rB^2

=> Area of A = 4 Area of B
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Re: The circumference of Circle A is twice the circumference of [#permalink]
02 Nov 2020, 04:31
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