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# A 45° arc of circle A is equal in length to a 30° arc of circle B. Wha

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Math Expert
Joined: 02 Sep 2009
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A 45° arc of circle A is equal in length to a 30° arc of circle B. Wha  [#permalink]

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18 Mar 2019, 02:43
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Difficulty:

55% (hard)

Question Stats:

53% (01:32) correct 47% (01:53) wrong based on 45 sessions

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A 45° arc of circle A is equal in length to a 30° arc of circle B. What is the ratio of circle A's area and circle B's area?

(A) 4/9
(B) 2/3
(C) 5/6
(D) 3/2
(E) 9/4

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Re: A 45° arc of circle A is equal in length to a 30° arc of circle B. Wha  [#permalink]

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18 Mar 2019, 02:48
Bunuel wrote:
A 45° arc of circle A is equal in length to a 30° arc of circle B. What is the ratio of circle A's area and circle B's area?

(A) 4/9
(B) 2/3
(C) 5/6
(D) 3/2
(E) 9/4

45/360 * 2*pi * r1= 30/360 * 2* pi * r2
we get
15r1= r2
so
area ratio = pi * r1^2/ pi * 15*15 * r1^2 = 4/9
IMO A
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Joined: 12 Sep 2017
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Re: A 45° arc of circle A is equal in length to a 30° arc of circle B. Wha  [#permalink]

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15 Jun 2019, 09:06
Can someone give an explianed answer please?

Kind regards!
VP
Joined: 19 Oct 2018
Posts: 1314
Location: India
Re: A 45° arc of circle A is equal in length to a 30° arc of circle B. Wha  [#permalink]

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15 Jun 2019, 09:23
let radius of of circle A= a, and radius of circle B= b.

Circumference of the 45° arc of circle A= $$\frac{45}{360}$$*2*pi*a
Circumference of the 30° arc of circle B= $$\frac{30}{360}*2*pi*b$$
$$\frac{45}{360}*2*pi*a$$ = $$\frac{30}{360}*2*pi*b$$
3a=2b
$$\frac{a}{b}=\frac{2}{3}$$

Area of circle A= $$pi*a^2$$
Area of circle B= $$pi*b^2$$

Area of circle A/Area of circle B= $$\frac{a^2}{b^2}$$=4/9

jfranciscocuencag wrote:
Can someone give an explianed answer please?

Kind regards!
VP
Joined: 20 Jul 2017
Posts: 1337
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: A 45° arc of circle A is equal in length to a 30° arc of circle B. Wha  [#permalink]

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15 Jun 2019, 09:33
Bunuel wrote:
A 45° arc of circle A is equal in length to a 30° arc of circle B. What is the ratio of circle A's area and circle B's area?

(A) 4/9
(B) 2/3
(C) 5/6
(D) 3/2
(E) 9/4

Length of Arc of a circle = (θ/360)*2πr

Let the radius of circle A = a
Radius of circle B = b

45° arc of circle A is equal in length to a 30° arc of circle B
—> 45/360*2πa = 30/360*2πb
—> 45a = 30b
—> a/b = 30/45 = 2/3

$$\frac{(Area of circle A)}{(Area of circle B)}$$ = $$πa^2/πb^2$$
= $$(a/b)^2$$
= $$(2/3)^2$$
= 4/9

IMO Option A

Pls Hit kudos if you like the solution

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Re: A 45° arc of circle A is equal in length to a 30° arc of circle B. Wha   [#permalink] 15 Jun 2019, 09:33
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# A 45° arc of circle A is equal in length to a 30° arc of circle B. Wha

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