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27 Oct 2021, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (01:27) correct
21%
(01:13)
wrong
based on 39
sessions
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The length and width of a rectangular box are 6 feet and 5 feet, respectively. A hose supplies water at a rate of 6 cubic feet per minute. How long would it take to fill a conical box whose volume is three times the volume of the rectangle box?
(1) The depth of the rectangular box is 7 feet.
(2) The radius of the base of the conical box is 6 feet.
(1) The depth of the rectangular box is 7 feet.
(2) The radius of the base of the conical box is 6 feet.
27 Oct 2021, 04:27
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Bunuel
Solution:
Length of rectangular box \(= 6\) feet. Breadth of rectangular box \(= 5\) feet. And let us assume the height of the rectangular box be \(h\) feet.
So, volume of rectangular box \(= 6\times 5\times h=30h feet^3\)
Volume of conical box \(= 3\times V_{rectangular box}=3\times 30h=90h feet^3\)
Speed of water from hose \(= 6 feet^3/min\).
Thus, time to fill conical box \(= \frac{V_{conicalbox}}{Speed} = \frac{90h}{6}\) minutes.
Now, to get the answer, we need the value of \(h\).
Statement 1:
This statement gives us depth or height of rectangular box \(= h = 7\).
This is exactly what we needed to get our answer.
Thus, statement 1 alone is sufficient. We can eliminate options B, C and E.
Statement 2:
This statement tells us the radius of the base of the conical box.
However, this is not sufficient to get the value of conical box.
We either need height of conical box or the slant height.
Statemment 2 alone is not sufficient.
Hence the right answer is Option A.
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