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Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.
Q. How many cubelets are there which are colored with exactly one color?
- a)180
- b)150
- c)165
- d)148
Correct answer is option 'C'. Can you explain this answer?
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Direction : A cube is divided into 343 identical cubelets. Each cut is...
From each face 5 x 5 = 25 cubelets are painted is one color. Such total = 25 x 6 = 150 cubelets. Further because each face Is having one similar color adjacent face and 3 other different coloured faces hence 5 x 3 = 15 extra cubelets will come from three edges, where adjacent faces of similar color are meeting hence total = 150 + 15 = 165 cube will be then colored in exactly one color
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Direction : A cube is divided into 343 identical cubelets. Each cut is...
Given information:
- A cube is divided into 343 identical cubelets.
- Each cut is made parallel to some surface of the cube.
- The cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.
To find:
- How many cubelets are there which are colored with exactly one color?
Solution:
Total number of cubelets = 343
Let's consider each color separately:
Green color:
- There are 7 layers of cubelets in the cube.
- Each layer has 7 x 7 cubelets.
- The cubelets on the outermost layer have two faces colored green.
- The cubelets on the second layer have one face colored green.
- The cubelets on the innermost layer have no faces colored green.
Therefore, the total number of cubelets colored green = (5 x 5 x 2) + (5 x 4 x 2) + (5 x 3 x 2) + (5 x 2 x 2) + (5 x 1 x 2) = 150
Similarly, we can find the number of cubelets colored red and blue:
Red color:
- The cubelets on the outermost layer have two faces colored red.
- The cubelets on the second layer have one face colored red.
- The cubelets on the innermost layer have no faces colored red.
Therefore, the total number of cubelets colored red = (5 x 5 x 2) + (5 x 4 x 2) + (5 x 3 x 2) + (5 x 2 x 2) + (5 x 1 x 2) = 150
Blue color:
- The cubelets on the outermost layer have two faces colored blue.
- The cubelets on the second layer have one face colored blue.
- The cubelets on the innermost layer have no faces colored blue.
Therefore, the total number of cubelets colored blue = (5 x 5 x 2) + (5 x 4 x 2) + (5 x 3 x 2) + (5 x 2 x 2) + (5 x 1 x 2) = 150
Now, we need to find the number of cubelets that are colored with exactly one color.
- Cubelets colored only green = 150 - 25 (cubelets with two green faces) - 50 (cubelets with one green face and one face of another color) = 75
- Cubelets colored only red = 75
- Cubelets colored only blue = 75
Therefore, the total number of cubelets colored with exactly one color = 75 + 75 + 75 = 225
But we have counted cubelets with two colors twice.
- Cubelets with two green faces and one face of another color = 25
- Cubelets with two red faces and one face of another color = 25
- Cubelets with two blue faces and one face of another color = 25
Therefore, we need to subtract 25 x 3 = 75 from 225.
Final answer:
- Number of cubelets colored with exactly one color = 225 - 75 = 150
Hence
- A cube is divided into 343 identical cubelets.
- Each cut is made parallel to some surface of the cube.
- The cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.
To find:
- How many cubelets are there which are colored with exactly one color?
Solution:
Total number of cubelets = 343
Let's consider each color separately:
Green color:
- There are 7 layers of cubelets in the cube.
- Each layer has 7 x 7 cubelets.
- The cubelets on the outermost layer have two faces colored green.
- The cubelets on the second layer have one face colored green.
- The cubelets on the innermost layer have no faces colored green.
Therefore, the total number of cubelets colored green = (5 x 5 x 2) + (5 x 4 x 2) + (5 x 3 x 2) + (5 x 2 x 2) + (5 x 1 x 2) = 150
Similarly, we can find the number of cubelets colored red and blue:
Red color:
- The cubelets on the outermost layer have two faces colored red.
- The cubelets on the second layer have one face colored red.
- The cubelets on the innermost layer have no faces colored red.
Therefore, the total number of cubelets colored red = (5 x 5 x 2) + (5 x 4 x 2) + (5 x 3 x 2) + (5 x 2 x 2) + (5 x 1 x 2) = 150
Blue color:
- The cubelets on the outermost layer have two faces colored blue.
- The cubelets on the second layer have one face colored blue.
- The cubelets on the innermost layer have no faces colored blue.
Therefore, the total number of cubelets colored blue = (5 x 5 x 2) + (5 x 4 x 2) + (5 x 3 x 2) + (5 x 2 x 2) + (5 x 1 x 2) = 150
Now, we need to find the number of cubelets that are colored with exactly one color.
- Cubelets colored only green = 150 - 25 (cubelets with two green faces) - 50 (cubelets with one green face and one face of another color) = 75
- Cubelets colored only red = 75
- Cubelets colored only blue = 75
Therefore, the total number of cubelets colored with exactly one color = 75 + 75 + 75 = 225
But we have counted cubelets with two colors twice.
- Cubelets with two green faces and one face of another color = 25
- Cubelets with two red faces and one face of another color = 25
- Cubelets with two blue faces and one face of another color = 25
Therefore, we need to subtract 25 x 3 = 75 from 225.
Final answer:
- Number of cubelets colored with exactly one color = 225 - 75 = 150
Hence
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Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer?
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Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer?.
Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer?.
Solutions for Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.Q. How many cubelets are there which are colored with exactly one color?a)180b)150c)165d)148Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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