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23 May 2023, 01:30
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
54% (01:55) correct
46%
(01:49)
wrong
based on 54
sessions
History
Date
Time
Result
Not Attempted Yet
How many perfectly spherical balloons of 1-foot radius can fit in a room that is 10 feet wide by 12 feet long by 8 feet high without compressing any of the balloons or allowing any balloon to touch more than 6 other balloons?
A. 30
B. 120
C. 144
D. 360
E. 960
A. 30
B. 120
C. 144
D. 360
E. 960
23 May 2023, 15:19
Kudos
Bookmarks
Bunuel
We can place 6 balloons along the length of the rectangular box, 5 balloons along the length of the rectangular box, and 4 balloons along the height of the rectangular box. So total number of balloons = 4 * 5 * 6 = 120
Option B
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23 May 2023, 20:17
Kudos
Bookmarks
The diameter of a balloon is 2 feet. So the number of balloons that can fit in the room is (10/2)*(12/2)*(8/2) = 5*6*4 = 120
We are given that no balloon touches more than 6 other balloons. Each balloon can touch a maximum of 2 balloons at the front and back of it, 2 balloons to the left and right, and 2 balloons directly above or below it, for a maximum of 6 balloons.
So the answer is still 120. (B) is the correct answer.
We are given that no balloon touches more than 6 other balloons. Each balloon can touch a maximum of 2 balloons at the front and back of it, 2 balloons to the left and right, and 2 balloons directly above or below it, for a maximum of 6 balloons.
So the answer is still 120. (B) is the correct answer.
