UPSC Exam > UPSC Questions > A cube has all its faces painted with differe...
Start Learning for Free
A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:
- a)32
- b)24
- c)16
- d)8
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A cube has all its faces painted with different colours. It is cut int...
(d) The number of small cubes with only one of the sides painted is 8.
Most Upvoted Answer
A cube has all its faces painted with different colours. It is cut int...
Solution:
Given, a cube is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.
Let the side of the big cube be 'a'. Then, the side of the small cube is 'a/4'.
The number of small cubes in each row of the big cube is 'a/(a/4)' = 4.
Therefore, the total number of small cubes in the big cube is 4 x 4 x 4 = 64.
Now, we need to find the number of small cubes with only one of the sides painted.
There are 8 corner cubes in the big cube. Each corner cube has 3 sides painted.
There are 12 edge cubes in the big cube. Each edge cube has 2 sides painted.
There are 6 face cubes in the big cube. Each face cube has 1 side painted.
So, the total number of small cubes with only one of the sides painted is:
8 x 3 + 12 x 2 + 6 x 1 = 24 + 24 + 6 = 54
But each small cube has 6 faces. So, we need to divide the total by 6 to get the number of small cubes.
Therefore, the number of small cubes with only one of the sides painted is:
54/6 = 9
Hence, the correct option is (D) 8.
Given, a cube is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.
Let the side of the big cube be 'a'. Then, the side of the small cube is 'a/4'.
The number of small cubes in each row of the big cube is 'a/(a/4)' = 4.
Therefore, the total number of small cubes in the big cube is 4 x 4 x 4 = 64.
Now, we need to find the number of small cubes with only one of the sides painted.
There are 8 corner cubes in the big cube. Each corner cube has 3 sides painted.
There are 12 edge cubes in the big cube. Each edge cube has 2 sides painted.
There are 6 face cubes in the big cube. Each face cube has 1 side painted.
So, the total number of small cubes with only one of the sides painted is:
8 x 3 + 12 x 2 + 6 x 1 = 24 + 24 + 6 = 54
But each small cube has 6 faces. So, we need to divide the total by 6 to get the number of small cubes.
Therefore, the number of small cubes with only one of the sides painted is:
54/6 = 9
Hence, the correct option is (D) 8.
Free Test
FREE
| Start Free Test |
Community Answer
A cube has all its faces painted with different colours. It is cut int...
Yes sir answer is 24
each side is painted different color
they said that small cube side is one fourth of the big cube side
ex: if we consider four equal distances in that large cube side then the small cube side is one fourth of the big cube so that there are 16 boxes were formed in the big cube side
12 are painted with colors and four are painted with single color
like there are 6 faces in a cube. each side there are four single colored
totally 6×4 = 24
each side is painted different color
they said that small cube side is one fourth of the big cube side
ex: if we consider four equal distances in that large cube side then the small cube side is one fourth of the big cube so that there are 16 boxes were formed in the big cube side
12 are painted with colors and four are painted with single color
like there are 6 faces in a cube. each side there are four single colored
totally 6×4 = 24
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer?
Question Description
A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer?.
A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer?.
Solutions for A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube.The number of small cubes with only one of the sides painted is:a)32b)24c)16d)8Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup