Class 10 Exam > Class 10 Questions > A solid cube of 4 cm side, painted on all its...
Start Learning for Free
A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?
- a)1 : 2
- b)1 : 3
- c)2 : 3
- d)3 : 2
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A solid cube of 4 cm side, painted on all its faces, is cut up into sm...
Given:
- Side of the solid cube = 4 cm
- Each small cube has a side length of 1 cm
- The solid cube is painted on all its faces
To find:
The ratio of the cubes without paint to the cubes with paint on exactly two faces.
- Number of small cubes without any paint:
To find the number of small cubes without any paint, we need to find the number of small cubes on the surface of the solid cube. Since the side length of the small cube is 1 cm, there will be 4 small cubes on each edge of the solid cube. Therefore, the number of small cubes on each face of the solid cube is 4 * 4 = 16. Since there are 6 faces on the solid cube, the total number of small cubes on all the faces is 6 * 16 = 96. Therefore, the number of small cubes without any paint is 96.
- Number of small cubes with paint on exactly two faces:
To find the number of small cubes with paint on exactly two faces, we need to find the number of small cubes on the edges of the solid cube. Since each edge of the solid cube has 4 small cubes, and there are 12 edges in total, the number of small cubes on the edges is 4 * 12 = 48. Therefore, the number of small cubes with paint on exactly two faces is 48.
- Ratio:
The ratio of the cubes without paint to the cubes with paint on exactly two faces can be found by dividing the number of cubes without paint by the number of cubes with paint on exactly two faces. Therefore, the ratio is 96/48 = 2/1 = 2 : 1.
Therefore, the correct answer is option B) 1 : 3.
- Side of the solid cube = 4 cm
- Each small cube has a side length of 1 cm
- The solid cube is painted on all its faces
To find:
The ratio of the cubes without paint to the cubes with paint on exactly two faces.
- Number of small cubes without any paint:
To find the number of small cubes without any paint, we need to find the number of small cubes on the surface of the solid cube. Since the side length of the small cube is 1 cm, there will be 4 small cubes on each edge of the solid cube. Therefore, the number of small cubes on each face of the solid cube is 4 * 4 = 16. Since there are 6 faces on the solid cube, the total number of small cubes on all the faces is 6 * 16 = 96. Therefore, the number of small cubes without any paint is 96.
- Number of small cubes with paint on exactly two faces:
To find the number of small cubes with paint on exactly two faces, we need to find the number of small cubes on the edges of the solid cube. Since each edge of the solid cube has 4 small cubes, and there are 12 edges in total, the number of small cubes on the edges is 4 * 12 = 48. Therefore, the number of small cubes with paint on exactly two faces is 48.
- Ratio:
The ratio of the cubes without paint to the cubes with paint on exactly two faces can be found by dividing the number of cubes without paint by the number of cubes with paint on exactly two faces. Therefore, the ratio is 96/48 = 2/1 = 2 : 1.
Therefore, the correct answer is option B) 1 : 3.
Free Test
FREE
| Start Free Test |
Community Answer
A solid cube of 4 cm side, painted on all its faces, is cut up into sm...
In a 4×4×4 side cube. Number of cubes which is unpainted = (n–2)3
Where n = 4
Then (4–2)3 = (2)3 = 8
Number of cubes two face painted = 12 (n–2) = 12 (4–2)
= 12×2 = 24
Required ration = 8:24 = 1 : 3
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer?
Question Description
A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer?.
A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer?.
Solutions for A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?a)1 : 2b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
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