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Math Expert
Joined: 02 Sep 2009
Posts: 61484

The outside surface of a white cube with a volume 64 is painted purple
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04 Dec 2019, 00:16
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The outside surface of a white cube with a volume 64 is painted purple. The cube is then cut evenly into smaller 2x2x2 cubes. such that the sides that originally faced outside will remain white. What is the ratio of the total purple surface area and the total white surface area of the smaller cubes ? A. 3:1 B. 2:1 C. 1:1 D. 1:2 E. 1:3 Are You Up For the Challenge: 700 Level Questions
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Joined: 26 Jun 2017
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Re: The outside surface of a white cube with a volume 64 is painted purple
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04 Dec 2019, 08:27
Volume of Original cube : 64 units Volume of smaller cube : 8 units
No. of Smaller cubes after cut = 64/8 = 8 cubes
all of the 8 cubes will be corner cubes and each of them will have 3 sides which were originally facing outside(White color). So the remaining 3 sides will be of purple color.
In other words, 3 faces of a cube has white color and rest of the 3 has purple color therefore, 1:1 is the answer



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Joined: 03 Nov 2019
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Re: The outside surface of a white cube with a volume 64 is painted purple
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04 Dec 2019, 00:50
Now total number of cubes of sides 2x2x2 that can be formed from the cube of volume 64= 64/(2*2*2) =8 Total number of sides of smaller cubes combined= 6*8=48 Sides painted white: Total number of sides of smaller cube facing outside = 4*6 (i.e. 4 faces of smaller cubes per 1 face of larger cube* Total number of sides of larger cube) = 24 Sides painted Purple: Total number of sides of smaller cube facing inside = 48 24=24
total purple surface area/ total white surface area of the smaller cubes = 24*(2*2)/24*(2*2) = 1:1
Answer: C




Re: The outside surface of a white cube with a volume 64 is painted purple
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04 Dec 2019, 00:50






