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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 of these cubes that were originally not facing outside 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
A. 3:1
B. 2:1
C. 1:1
D. 1:2
E. 1:3
Are You Up For the Challenge: 700 Level Questions
Ansh777
Joined: 03 Nov 2019
Last visit: 06 Jun 2023
Posts: 57
Given Kudos: 129
Location: India
Schools: Booth '24 Columbia CBS '24 Darden '24 Fuqua '24 Haas '24 Harvard '24 LBS '24 Stanford '24 Kellogg '24 Wharton '24
GMAT 1: 710 Q50 V36
Schools: Booth '24 Columbia CBS '24 Darden '24 Fuqua '24 Haas '24 Harvard '24 LBS '24 Stanford '24 Kellogg '24 Wharton '24
GMAT 1: 710 Q50 V36
Posts: 57
04 Dec 2019, 01:50
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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
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
04 Dec 2019, 09:27
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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
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
