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15 Nov 2018, 04:15
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C
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:
73% (01:24) correct
27%
(01:52)
wrong
based on 95
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If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?
A. \(\frac{2}{\pi}\)
B. \(\frac{\pi}{4}\)
C. \(\frac{4}{\pi}\)
D. \(\frac{\pi}{2}\)
E. 4
A. \(\frac{2}{\pi}\)
B. \(\frac{\pi}{4}\)
C. \(\frac{4}{\pi}\)
D. \(\frac{\pi}{2}\)
E. 4
15 Nov 2018, 04:26
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Solution
Given:
- • Radius of the cylinder = \((\frac{1}{2})\) * length of the edge of a cube
• Height of the cylinder = length of the edge of the cube
To find:
- • The ratio of volumes of cube and cylinder
Approach and Working:
- • Volume of cube = \(a^3\), where a is the side length
• Volume of cylinder = \(ᴨ * r^2 * h\), where r is radius and h is the height
Given that, \(r = \frac{a}{2}\) and h = a
- • Implies, volume of cylinder = \(ᴨ * (\frac{a}{2})^2 * a = ᴨ * \frac{a^3}{4} = (\frac{ᴨ}{4})\) * volume of the cube
Therefore, ratio of volume of cube to the volume of cylinder = \(\frac{4}{ᴨ}\)
Hence, the correct answer is Option C
Answer: C
15 Nov 2018, 04:36
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Bunuel
Let side of cube be 2
So radius will be 1 and height will be 2
Volume of cube = s^3 = 2^3 = 8
Volume of cylinder = pi r^2 * h = pi * 1 * 2
8/(2*pi) = 4/pi
Answer choice C
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