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505-555 (Easy)|   Geometry|      
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Bunuel
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Three metal cubes with edges of two will be dropped into an empty cyli 17 Jan 2019, 03:15
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15% (low)

Question Stats:

88% (01:33) correct 12% (01:37) wrong based on 31 sessions

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Three metal cubes with edges of two will be dropped into an empty cylindrical tank with a base radius of 3 and a height of 8. The three cubes will take up what fraction of the volume of the tank?


A 1/3

B 1/π

C 3/π

D 1/(3π)

E 2/(3π)
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D
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Three metal cubes with edges of two will be dropped into an empty cyli 17 Jan 2019, 03:22
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Volume of a cube = \(side^3\)
Volume of each cube = 2*2*2 = 8
Volume of 3 cubes = 8*3 = 24

Volume of the cylinder = \(π*r^2*h\) = π*9*8 = 72π

24/72π = 1/3π

Bunuel, π is missing in option A.
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Three metal cubes with edges of two will be dropped into an empty cyli 17 Jan 2019, 03:27
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Afc0892
Volume of a cube = \(side^3\)
Volume of each cube = 2*2*2 = 8
Volume of 3 cubes = 8*3 = 24

Volume of the cylinder = \(π*r^2*h\) = π*9*8 = 72π

24/72π = 1/3π

Bunuel, π is missing in option A.
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Formatting error. Edited. Thank you.
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Three metal cubes with edges of two will be dropped into an empty cyli 17 Jan 2019, 03:48
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Dear Afc0892 Bunuel

Why you assumed that "base" is radius and not diameter? :?


Regards
L
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Three metal cubes with edges of two will be dropped into an empty cyli 17 Jan 2019, 03:51
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LevanKhukhunashvili
Dear Afc0892 Bunuel

Why you assumed that "base" is radius and not diameter? :?


Regards
L
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__________________
Edited to make it clear.
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Three metal cubes with edges of two will be dropped into an empty cyli 17 Jan 2019, 03:52
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LevanKhukhunashvili
Dear Afc0892 Bunuel

Why you assumed that "base" is radius and not diameter? :?


Regards
L
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I had the same doubt. But I checked by considering the base as diameter and there were not any options. So concluded that it should be radius.

Bunuel sir, If you could edit the question. It'll help to understand better.

Posted from my mobile device
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Three metal cubes with edges of two will be dropped into an empty cyli 17 Jan 2019, 06:32
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Bunuel
Three metal cubes with edges of two will be dropped into an empty cylindrical tank with a base radius of 3 and a height of 8. The three cubes will take up what fraction of the volume of the tank?


A 1/3

B 1/π

C 3/π

D 1/(3π)

E 2/(3π)
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vol of cyld : pi * r^2 * h = 9*8*pi = 72 pi
volf of 3 cubes : 2^3 * 3 = 24
so area of cube would be be 24/72 Pi = 1/ 3pi
IMO D
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Three metal cubes with edges of two will be dropped into an empty cyli 17 Jan 2019, 07:22
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Bunuel
Three metal cubes with edges of two will be dropped into an empty cylindrical tank with a base radius of 3 and a height of 8. The three cubes will take up what fraction of the volume of the tank?


A 1/3

B 1/π

C 3/π

D 1/(3π)

E 2/(3π)
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IMO D

Given
side of cube = 2

Volume = side^3 = 8

Volume of 3 cubes =24

Volume of cylinder = π * 8 * 9 = 72 π

Fraction = Volume of 3 cubes / Volume of cylinder

= 1 / 3π
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