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29 Jul 2022, 06:30
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A
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Difficulty:
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79% (01:43) correct
21%
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Is the length of the longest line that can be drawn inside a cube greater than the length of the longest line that can be drawn inside a right circular cylinder?
(1) Each side of the cube is half the height of the cylinder but twice the radius of the cylinder.
(2) The sum of the lengths of the radius of cylinder, the height of the cylinder and a side of the cube is 14
(1) Each side of the cube is half the height of the cylinder but twice the radius of the cylinder.
(2) The sum of the lengths of the radius of cylinder, the height of the cylinder and a side of the cube is 14
29 Jul 2022, 06:57
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Bunuel
Is the length of the longest line that can be drawn inside a cube greater than the length of the longest line that can be drawn inside a right circular cylinder?
(1) Each side of the cube is half the height of the cylinder but twice the radius of the cylinder.
(2) The sum of the lengths of the radius of cylinder, the height of the cylinder and a side of the cube is 14
(1) Each side of the cube is half the height of the cylinder but twice the radius of the cylinder.
(2) The sum of the lengths of the radius of cylinder, the height of the cylinder and a side of the cube is 14
Let the side of the cube = a
The longest line that can be drawn inside a cube = \(\sqrt{a^2 + a^2 + a^2}\) = \(\sqrt{3a^2}\) = \(a\sqrt{3}\)
And let the radius and height of the cylinder = r and h (respectively)
Longest side that can be drawn is a straight line from top to bottom covering both diameters and the height = h+2d = h+4r
We need to determine if \(a\sqrt{3}\) > \(h + 4r\) ?
(1) Each side of the cube is half the height of the cylinder but twice the radius of the cylinder.
\(h = 2a\)
\(r = 0.5a\)
\(h + 4r = 4a\)
Therefore we need to find if: \(a\sqrt{3}\) > \(4a\)
Irrespective of what the value of \(a\) is, this above condition will ALWAYS BE FALSE
SUFFICIENT
(2) The sum of the lengths of the radius of cylinder, the height of the cylinder and a side of the cube is 14
\(h + r + a = 14\)
If \(a = 4\), \(h = 6\) and \(r = 4\) => Is \(4\sqrt{3}\) > \(22\) NO
If \(a = 10\), \(h = 3\) and \(r = 1\) => Is \(10\sqrt{3}\) > \(7\) YES
NOT SUFFICIENT
Answer - A
