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Strange question. help pls.

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Strange question. help pls.

by tanviet » Fri Oct 30, 2009 5:29 am
this is from 15 testset.

on an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. if a distance of 1 inch on the photogragh corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles.

a,1.3
b,2.4
c,3.0
d,3.8
e,5.0
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by BuckeyeT » Fri Oct 30, 2009 6:38 am
r= 7/16 in
1 in = 2 miles

r = (7/16) in * (2 miles / 1 in)
r = 7/8 miles

A = pi * r^2
A = ~3 * (7/8)^2
A = ~3 * 49/64
A = ~ 147/64
A = 2.something

Only one answer is in this area: B.
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by NikolayZ » Fri Oct 30, 2009 6:43 am
In this problem, you need to convert photo scale into the actual sclae. i.e. the radius of photo to the radius of actual place in the air.
s0, 7/16*2=14/16.
knowing the formula of the area of the cirlce - (pi)r^2
the area will be - 196/256(pi) ( pi=3.14 so it would be approximately 3)
after simplification - 49/64*(pi), round both numerator and denominator to the closest number.
50/65*3=10/13*3=30/13, approximately 2.3 smth.
so the answer should be b.
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