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hard 2 get through,,

by sumasajja » Fri Jul 22, 2011 12:10 am
28. One hose dispenses water at the rate of 1 gallon per minute, and a second hose
dispenses water at the rate of 1 1\2 gallons per minute.
At the same time, the two hoses begin filling a cylindrical pail whose diameter is
14 inches and whose height is 10 inches. Which of the following most closely
approximates the water level, measured in inches up from the pail's circular
base, after 1 1\2 minutes? [231 cubic inches 5=1 gallon]
(A) 3.5
(B) 4.2
(C) 4.8
(D) 5.6
(E) 6.7
The correct answer is (D).
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by knight247 » Fri Jul 22, 2011 12:51 am
Volume of cylinder = pi*r^2*h
given that D=14 so R=7 and h=14inches

Hose A
in 1 minute fills one gallon
in 1.5 minutes fills 1.5 gallons

Hose B
in 1 minute fills 1.5 gallons
in 1.5 minutes fills 2.25 gallons

After 1.5 minutes the total volume of water filled in the pail is 3.75 gallons

Now the portion of the cylinder filled with water can be considered a new cylinder
having volume =3.75 gallons h=? and r=7 inches (as the base stays the same for both cylinders)
Converting volume from gallons to cubic inches we get volume =3.75*231 cu.inches


Substituting these values in the formula

Volume of cylinder = pi*r^2*h

we get

3.75*231=(pi)(7^2)(h)
h=(3.75*231)/(pi*49)
h=5.6

Hence D
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