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Integrated Reasoning : Two part analysis

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Integrated Reasoning : Two part analysis [#permalink] New post 09 Sep 2012, 15:35
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“An architect is planning to incorporate several stone spheres of different sizes into the landscaping of a public park, and workers who will be applying a finish to the exterior of the spheres need to know the surface area of each sphere. The finishing process costs $92 per square meter. The surface area of a sphere is equal to 4πr2, where r is the radius of the sphere.

“In the table, select the value that is closest to the cost of finishing a sphere with a 5.50-meter circumference as well as the cost of finishing a sphere with a 7.85-meter circumference. Make only two selections, one in each column.”

Circumference 5.50 m Circumference 7.85 m

Finishing cost
$900

$1,200

$1,800

$2,800

$3,200

$4,500

[Reveal] Spoiler:
5.5 m = $900, 7.85 m = 1800
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Re: Integrated Reasoning : Two part analysis [#permalink] New post 09 Sep 2012, 18:33
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1. 2πr=5.50
=> r = 5.5/2π = 5.5/2x3.14 = .875
So surface area = 4πr^2= 4x3.14x .875^2 = 9.61 m^2
Hence cost = 9.61x92 = 885 ~ $900
2. 2πr=7.85
=> r = 7.85/2π = 7.85/2x3.14 = 1.25
So surface area = 4πr^2= 4x3.14x 1.25^2 = 19.625 m^2
Hence cost = 19.625x92 = 1805 ~ $1800
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Re: Integrated Reasoning : Two part analysis [#permalink] New post 03 Oct 2012, 23:45
Circumference = 2πr
Surface Area of Sphere = 4π(r^2) = (Circumference^2)/π
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Re: Integrated Reasoning : Two part analysis   [#permalink] 03 Oct 2012, 23:45
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