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A big cube is having 20 cm portion and the tiny cubes cut out of it is having 4 cm of each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes?
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A big cube is having 20 cm portion and the tiny cubes cut out of it is...
To determine how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes, let's break down the problem step by step.
Step 1: Calculating the Number of Tiny Cubes
- The big cube has a side length of **20 cm**.
- Each tiny cube has a side length of **4 cm**.
To find out how many tiny cubes fit into the big cube, we can use the formula:
- Number of tiny cubes = (Side length of big cube / Side length of tiny cube)³
Calculating this:
- Number of tiny cubes = (20 cm / 4 cm)³ = 5³ = **125** tiny cubes.
Step 2: Identifying Surrounding Cubes
Next, we need to find out how many of these tiny cubes are surrounded on all sides by other cubes.
- The cubes that are not surrounded are those on the outermost layer of the big cube.
To find the number of cubes that are surrounded, consider the inner volume:
- The inner layer of cubes can be calculated by reducing the outer layer by 1 cube on each side:
- New side length = 5 - 2 = 3 (since we remove 1 layer from each side).
Calculating the number of inner cubes:
- Number of inner cubes = 3³ = **27** cubes.
Step 3: Conclusion
- Therefore, the number of tiny cubes that are surrounded on all faces by other cubes is **27**.
This detailed analysis shows how many tiny cubes are completely surrounded in the big cube structure.
Step 1: Calculating the Number of Tiny Cubes
- The big cube has a side length of **20 cm**.
- Each tiny cube has a side length of **4 cm**.
To find out how many tiny cubes fit into the big cube, we can use the formula:
- Number of tiny cubes = (Side length of big cube / Side length of tiny cube)³
Calculating this:
- Number of tiny cubes = (20 cm / 4 cm)³ = 5³ = **125** tiny cubes.
Step 2: Identifying Surrounding Cubes
Next, we need to find out how many of these tiny cubes are surrounded on all sides by other cubes.
- The cubes that are not surrounded are those on the outermost layer of the big cube.
To find the number of cubes that are surrounded, consider the inner volume:
- The inner layer of cubes can be calculated by reducing the outer layer by 1 cube on each side:
- New side length = 5 - 2 = 3 (since we remove 1 layer from each side).
Calculating the number of inner cubes:
- Number of inner cubes = 3³ = **27** cubes.
Step 3: Conclusion
- Therefore, the number of tiny cubes that are surrounded on all faces by other cubes is **27**.
This detailed analysis shows how many tiny cubes are completely surrounded in the big cube structure.
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A big cube is having 20 cm portion and the tiny cubes cut out of it is having 4 cm of each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes?
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A big cube is having 20 cm portion and the tiny cubes cut out of it is having 4 cm of each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A big cube is having 20 cm portion and the tiny cubes cut out of it is having 4 cm of each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A big cube is having 20 cm portion and the tiny cubes cut out of it is having 4 cm of each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes?.
A big cube is having 20 cm portion and the tiny cubes cut out of it is having 4 cm of each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A big cube is having 20 cm portion and the tiny cubes cut out of it is having 4 cm of each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A big cube is having 20 cm portion and the tiny cubes cut out of it is having 4 cm of each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes?.
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