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07 Jun 2022, 01:30
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When 30 gallons of water is poured into a cylindrical tank whose sides are perpendicular to a flat base, the water level rises 0.5 foot. If 7.5 gallons of water occupies 1 cubic foot of space, then the base of the tank has an area of how many square feet? (volume of the tank = height x area of base)
(A) 37.5
(B) 8
(C) 4.5
(D) 4
(E) cannot be determined
Are You Up For the Challenge: 700 Level Questions
(A) 37.5
(B) 8
(C) 4.5
(D) 4
(E) cannot be determined
Are You Up For the Challenge: 700 Level Questions
07 Jun 2022, 03:03
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If 30 gallons of water results in water level rise of 0.5 foot.
7.5 gallons of water results in water level rise of
(7.5X0.5)/30=0.125
7.5 gallons of water occupies 1 cubic foot of space and
volume of the tank = height x area of base
So
1 = 0.125*BaseArea
BaseArea=1/0.125=8
The answer is (B).
7.5 gallons of water results in water level rise of
(7.5X0.5)/30=0.125
7.5 gallons of water occupies 1 cubic foot of space and
volume of the tank = height x area of base
So
1 = 0.125*BaseArea
BaseArea=1/0.125=8
The answer is (B).
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07 Jun 2022, 03:17
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\(7.5\) gallons occupies \(1\) cubic feet of area.
So, \(30\) gallon would occupy \(30/7.5\) cubic feet of area = volume occupied by 30 gallon in the cylinder. That volume is given by \(πr^2*h\), where \(h = 0.5 ft\).
Thus,
\(πr^2*0.5 = 30/7.5\)
We need to find the value of \(πr^2\),
So, \(πr^2 = 30/7.5 * 0.5 = 8\).
(B)
So, \(30\) gallon would occupy \(30/7.5\) cubic feet of area = volume occupied by 30 gallon in the cylinder. That volume is given by \(πr^2*h\), where \(h = 0.5 ft\).
Thus,
\(πr^2*0.5 = 30/7.5\)
We need to find the value of \(πr^2\),
So, \(πr^2 = 30/7.5 * 0.5 = 8\).
(B)
