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24 Dec 2020, 07:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
39% (01:36) correct
61%
(01:28)
wrong
based on 57
sessions
History
Date
Time
Result
Not Attempted Yet
The diagram below shows a cube 3 units on a side with a 1 × 1 square hole cut through it. How many square units is the total surface area of the cube?
(A) 52
(B) 54
(C) 60
(D) 64
(E) 66
Attachment:
2020-12-21_18-46-12.png [ 18.6 KiB | Viewed 2198 times ]
24 Dec 2020, 08:44
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Area of the cube \(= 6a^2 =6*3^2=6*9=54\)
Area of the smaller Square \(= a^2=1\)
Total number of smaller square are \(2\), i.e. \(2*1=2\)
Area of the cube after substracting smaller area \(=54-2=52\)
Now, the surface area of the inner cross section \(=3*1*4 =12\) (\(3\) is length of the section; \(4\) is the number of area of \(3*1\))
Total surface area \(=52+12=64\)
IMO Ans D
Area of the smaller Square \(= a^2=1\)
Total number of smaller square are \(2\), i.e. \(2*1=2\)
Area of the cube after substracting smaller area \(=54-2=52\)
Now, the surface area of the inner cross section \(=3*1*4 =12\) (\(3\) is length of the section; \(4\) is the number of area of \(3*1\))
Total surface area \(=52+12=64\)
IMO Ans D
Updated on: 28 Dec 2020, 20:10
Originally posted by TarunKumar1234 on 25 Dec 2020, 14:50.
Last edited by TarunKumar1234 on 28 Dec 2020, 20:10, edited 1 time in total.
Last edited by TarunKumar1234 on 28 Dec 2020, 20:10, edited 1 time in total.
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Surface area of Cube without square holes = 6*a^2 = 6*3^2 = 54
Square hole area= (1*1)*2= 2
Outer Surface are of cube with square holes = 54-2= 52
Due to across square hole, another surface area is exposed inside cube. Inside area= 4*3*1= 12
So, New Total Surface area of Cube = 52 +12 = 64
So, It is D.
Square hole area= (1*1)*2= 2
Outer Surface are of cube with square holes = 54-2= 52
Due to across square hole, another surface area is exposed inside cube. Inside area= 4*3*1= 12
So, New Total Surface area of Cube = 52 +12 = 64
So, It is D.
