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# The number of visible stars in the night sky, T, can be estimated by

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Math Expert
Joined: 02 Sep 2009
Posts: 59147
The number of visible stars in the night sky, T, can be estimated by  [#permalink]

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14 Aug 2019, 00:18
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Difficulty:

65% (hard)

Question Stats:

63% (02:33) correct 38% (02:56) wrong based on 80 sessions

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The number of visible stars in the night sky, T, can be estimated by the formula

$$T = (\frac{4\pi*L^2}{A})N$$

where N is the number of stars counted through a tube with length L, in centimeters, a mouth of area A, in square centimeters. Based on the formula, what is the estimated number of visible stars in the night sky if 240 stars are observed through a tube 10 feet long with a mouth of radius of 4 feet? (1 foot = 30.48 centimeters)

A. 182,880
B. 7,000
C. 6,000
D. 5,800
E. 500

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The number of visible stars in the night sky, T, can be estimated by  [#permalink]

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14 Aug 2019, 12:07
Bunuel wrote:
The number of visible stars in the night sky, T, can be estimated by the formula

$$T = (\frac{4\pi*L^2}{A})N$$

where N is the number of stars counted through a tube with length L, in centimeters, a mouth of area A, in square centimeters. Based on the formula, what is the estimated number of visible stars in the night sky if 240 stars are observed through a tube 10 feet long with a mouth of radius of 4 feet? (1 foot = 30.48 centimeters)

A. 182,880
B. 7,000
C. 6,000
D. 5,800
E. 500

L = 304.81 cm
A= 4*30.48 ; 121.92 cm and area ; pi * (121.92)^2 since its mouth would circular shape
N= 240
substitute values in

$$T = (\frac{4\pi*L^2}{A})N$$

$$T = (\frac{4\pi*(304.81)^2}{pi * (121.92)^2})240$$
T= ~6000 IMO C
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Joined: 24 Feb 2019
Posts: 54
Re: The number of visible stars in the night sky, T, can be estimated by  [#permalink]

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14 Aug 2019, 23:55
2
I would wait till the very last moment before doing any feet-cm conversion.
In fact, with hindsight, you notice that the conversion is only here to distract you, as it cancels out in the fraction.
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Re: The number of visible stars in the night sky, T, can be estimated by  [#permalink]

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19 Aug 2019, 19:22
2
Bunuel wrote:
The number of visible stars in the night sky, T, can be estimated by the formula

$$T = (\frac{4\pi*L^2}{A})N$$

where N is the number of stars counted through a tube with length L, in centimeters, a mouth of area A, in square centimeters. Based on the formula, what is the estimated number of visible stars in the night sky if 240 stars are observed through a tube 10 feet long with a mouth of radius of 4 feet? (1 foot = 30.48 centimeters)

A. 182,880
B. 7,000
C. 6,000
D. 5,800
E. 500

T = [(4π x (10 x 30.48)^2]/[(4 x 30.48)^2 x π] x 240

T = (4 x 10^2)/(4^2) x 240

T = 100/4 x 240

T = 100 x 60

T = 6,000

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Math Expert
Joined: 02 Sep 2009
Posts: 59147
Re: The number of visible stars in the night sky, T, can be estimated by  [#permalink]

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04 Oct 2019, 02:56
Bunuel wrote:
The number of visible stars in the night sky, T, can be estimated by the formula

$$T = (\frac{4\pi*L^2}{A})N$$

where N is the number of stars counted through a tube with length L, in centimeters, a mouth of area A, in square centimeters. Based on the formula, what is the estimated number of visible stars in the night sky if 240 stars are observed through a tube 10 feet long with a mouth of radius of 4 feet? (1 foot = 30.48 centimeters)

A. 182,880
B. 7,000
C. 6,000
D. 5,800
E. 500

Video Explanation

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Re: The number of visible stars in the night sky, T, can be estimated by   [#permalink] 04 Oct 2019, 02:56
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