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

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New post 15 Jul 2018, 07:20
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E

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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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New post 15 Jul 2018, 07:35
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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New post 15 Jul 2018, 11:14
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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New post 16 Jul 2018, 08:10
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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The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

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New post 19 Jul 2018, 07:20
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:
\(\frac{A}{B}=\frac{16 \pi}{9 \pi}=\frac{16}{9}=(16 : 9)\)

Answer 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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New post 19 Jul 2018, 11:36
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

Answer: E
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Re: The radius of circle A is r, and the radius of circle B is 3/4*r &nbs [#permalink] 19 Jul 2018, 11:36
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