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14 May 2021, 06:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
78% (02:09) correct
22%
(02:45)
wrong
based on 18
sessions
History
Date
Time
Result
Not Attempted Yet
A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described?
A. 16/π
B. 2π
C. 8
D. 4π
E. 8π
A. 16/π
B. 2π
C. 8
D. 4π
E. 8π
14 May 2021, 06:35
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Bunuel
Answer: Option D
Video solution by GMATinsight
14 May 2021, 08:53
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Bunuel
Attachment:
1.jpg [ 17.73 KiB | Viewed 1734 times ]
In the diagram, we observe:
Top view: Diameter of the circle (base of the cylinder) = side of the cube
=> Radius of the cylinder (r) = Side/2 ... (i)
Side view: Height of the cylinder (h) = height of the cube = Side ... (ii)
Volume of the cube = Side^3 = 16
Thus, volume of the cylinder = π * r^2 * h = π * (Side/2)^2 * (Side) = (π/4) * Side^3 = (π/4) * 16 = 4π
Answer D
Alternative:
Let us say, you are running out of time and you get this question. You do not have enough time to do all this.
How do you solve the question?
Clearly, the cylinder is INSIDE the cube, hence its volume will be less than the volume of the cube, i.e. 16.
From the TOP VIEW, it is clear that the circle takes up the major part of the square, hence, the volume of the cylinder will be greater than 50% of the cube, i.e. greater than 8.
Let us look at the options (assume pi = 3 approximately):
A: 16/π = 16/3 = 5.33 - less than half the volume, ignored
B. 2π = 2 * 3 = 6 - less than half the volume, ignored
C. 8 - exactly half the volume of the cube, ignored
D. 4π = 4 * 3 = 12 - GREATER than half the volume of the cube, possible
E. 8π = 8 * 3 = 24 - greater than the cube, ignored
Thus, only option D is possible
Answer D
Note: It is NOT about solving every time
