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There are two circle-shaped pizzas. The diameter of the smaller pizza

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There are two circle-shaped pizzas. The diameter of the smaller pizza  [#permalink]

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New post 16 Jun 2016, 20:35
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A
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Question Stats:

70% (01:32) correct 30% (01:35) wrong based on 131 sessions

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There are two circle-shaped pizzas. The diameter of the smaller pizza is 10 and the larger pizza’s area is 2 times of the smaller pizza’s area, what is the diameter of the larger pizza, in whole number?
A. 12
B. 15
C. 18
D. 20
E. 25

*An answer will be posted in 2 days.

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Re: There are two circle-shaped pizzas. The diameter of the smaller pizza  [#permalink]

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New post 16 Jun 2016, 21:28
Let the radius of the small pizza be r, and the radius of the bigger pizza be R. Given \(pi.r^2\) = \(pi.R^2\). Thus R ~ 1.41r. Therefore D = 1.41d as well. = 1.41*10 = 14.10. The nearest whole number from the answer choices is 15. Hence B.
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Re: There are two circle-shaped pizzas. The diameter of the smaller pizza  [#permalink]

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New post 16 Jun 2016, 22:30
MathRevolution wrote:
There are two circle-shaped pizzas. The diameter of the smaller pizza is 10 and the larger pizza’s area is 2 times of the smaller pizza’s area, what is the diameter of the larger pizza, in whole number?
A. 12
B. 15
C. 18
D. 20
E. 25

*An answer will be posted in 2 days.


Area of smaller pizza = (\(\pi\)\(10^2\))/ 4, where 10 is the dia of smaller circle.

Area of bigger pizza = twice of area of smaller pizza = (\(\pi\)\(10^2\))/ 2

if r is the radius of bigger pizza.

\(\pi\)\(r^2\) = (\(\pi\)\(10^2\))/ 2

\(r^2\) = 50

r = \(\sqrt{50}\)
diameter = 2r = 10\(\sqrt{2}\)

dia = 14.1416.

nearest value should have been 14. It is not given. So we will choose 15.
B is the answer.
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New post 19 Jun 2016, 17:48
Since √(proportion of area) = proportion of length. If the proportion of area is 2, then we have √2. Hence, the proportion of length becomes approximately 1.5. So, from 10*1.5=15. Thus, the correct answer is B.
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Re: There are two circle-shaped pizzas. The diameter of the smaller pizza   [#permalink] 27 Aug 2018, 07:03
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