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by Bhandaripreeti » Thu Sep 20, 2007 2:07 am
A straight semicircular tunnel with a width of 20 feet is carved into a mountain. The curved walls are to be painted white and the flat roadway is to be paved with asphalt. If one barrel of white paint can cover 40 square feet and an equal number of barrels of paint and barrels of asphalt are used, how many square feet must one barrel of asphalt cover?




1) Pi/4

2) 10 Pi

3) 80/Pi

4) 2

5) Cannot be determined from the information given
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by samirpandeyit62 » Thu Sep 20, 2007 2:22 am
IMO ans should be C 80/pi

given width of semicircular tunnel is 20 feet

ie. diameter is 20, so radius = 10

let lenght of tunnel be 'x'

so area of road = 20x

surface area of semicircular curve = pi*r*x = 10pi*x

now number of barrels of paint reqd for this curved surface = 10pi *x/40

=pi*x/4 = nos of barrels of asphalt reqd

so each barrel of asphalt covers 20x/(pi*x/4) = 80/pi
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Samir
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by kajcha » Thu Sep 20, 2007 5:33 am
80/pi for me too

assume length of the road/tunnel = x

surface area of circular portion = 2*pi*r*x/2 = pi*10*x = 10*pi*x

no of barrels used = 10*pi*x/40

no area of road = 20x

area covered per barrel of asphalt = 20x/(10*pi*x/40) = 80/pi
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by niks_01.27 » Thu Sep 20, 2007 7:53 pm
80 / pi for me too.

Excellent solutions are already posted. :wink:
regards
niks...
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