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24 Mar 2020, 09:54
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One hose dispenses water at the rate of one gallon per minute, and a second hose dispenses water at the rate of \(1\frac{1}{2}\) 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 \(1\frac{1}{2}\) minutes? [231 cubic inches = 1 gallon]
(A) 3.5
(B) 4.2
(C) 4.8
(D) 5.6
(E) 6.7
(A) 3.5
(B) 4.2
(C) 4.8
(D) 5.6
(E) 6.7
25 Mar 2020, 02:44
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SajjadAhmad
One hose dispenses water at the rate of one gallon per minute, and a second hose dispenses water at the rate of \(1\frac{1}{2}\) 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 \(1\frac{1}{2}\) minutes? [231 cubic inches = 1 gallon]
(A) 3.5
(B) 4.2
(C) 4.8
(D) 5.6
(E) 6.7
(A) 3.5
(B) 4.2
(C) 4.8
(D) 5.6
(E) 6.7
Solution:
- • Total water dispensed in one minute = \(1 + \frac{3}{2} =\frac{5}{2}\) gallons
- o Total water dispensed in 1 \(\frac{1}{2}\) minute = \(1 \frac{1}{2}*\frac{5}{2} =\frac{15}{4}\) gallon
o Total water dispensed in inch = \(\frac{15}{4 }*231\) cubic inch
Let h be the level of water in the tank after pouring \(\frac{15}{4 }*231\) cubic inches of water.
- • Volume of tank till the height \(h = π*r^2*h\)
- o \(\frac{15}{4 }*231 = \frac{22}{7}*7*7*h\)
o \(\frac{(15*231)}{(4*22*7)} = h\)
o\(\frac{(15*3)}{(4*2)} = h\)
o \(h = 5.625\) (approx.)
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