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# The radius of circle A is r, and the radius of circle B is 3/4*r

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15 Jul 2018, 08:20
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83% (00:47) correct 18% (01:44) wrong based on 49 sessions

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The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

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Re: The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

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15 Jul 2018, 08:35
Area of Circle A = π*r^2
Area of Circle B = π*(3/4*r)^2 = (π*r^2)*9/16

Ratio = Area of Circle A / Area of Circle B
= π*r^2 / (π*r^2)*9/16 ( Cancelling, π*r^2 from numerator and denominator)
= 1/(9/16)
= 16/9

Hence, E.
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Re: The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

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15 Jul 2018, 12:14
Bunuel wrote:
The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

Area of a circle = π $$r^2$$

Area of circle A = π$$r^2$$

Area of Circle B = π $$(3/4r)^2$$

Ratio = π $$r^2$$ / π $$(3/4r)^2$$

= r^2 / (9/16) $$r^2$$

= 1 / (9/16)

= 16 : 9

Thus the best answer is E.
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Re: The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

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16 Jul 2018, 09:10
Bunuel wrote:
The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

Ratio of the Area of Circles is actually the ratio of their Radii as $$πR^2 : πr^2 = R^2 : r^2$$

Thus, ratio of the Area of the circles is $$r^2 : (\frac{3}{4r})^2 = 16 : 9$$, Answer must be (E)
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19 Jul 2018, 08:20
Bunuel wrote:
The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

Let radius of $$A = 4$$
Radius of $$B =\frac{3}{4}A=(\frac{3}{4}*4)=3$$

Area of A: $$\pi r^2=\pi 4^2=16\pi$$
Area of B: $$\pi r^2=\pi 3^2=9\pi$$

Ratio of the area of circle A to the area of circle B:
$$\frac{A}{B}=\frac{16 \pi}{9 \pi}=\frac{16}{9}=(16 : 9)$$

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Re: The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

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19 Jul 2018, 12:36
Bunuel wrote:
The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

Area of circle A = πr^2

Area of circle B = π(¾ r)^2 = π(9/16)r^2

So the ratio of the area of circle A to the area of circle B is

πr^2/[π(9/16)r^2] = 1/(9/16) = 16/9

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Re: The radius of circle A is r, and the radius of circle B is 3/4*r   [#permalink] 19 Jul 2018, 12:36
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