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Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.
How many tiny cubes will be formed having one portion white and one portion green for sure?
18?
How many tiny cubes will be formed having one portion white and one portion green for sure?
18?
Most Upvoted Answer
Two adjacent portions of a big cube are varnished in green and their r...
Certainly! Let's analyze the problem step by step.
Understanding the Cube Structure
- The big cube is segmented into **125 tiny cubes**, indicating it is a **5x5x5 cube** (since \(5^3 = 125\)).
- The cube has **3 different colors**: green, white, and blue.
Color Distribution
- **Green Faces**: Two adjacent faces are painted green.
- **White Faces**: The opposite two faces of the green ones are painted white.
- **Blue Faces**: The remaining two faces are painted blue.
Finding Tiny Cubes with Green and White Faces
- The tiny cubes that have one face green and one face white must be located along the **edges** where the green and white faces meet.
Counting the Relevant Edges
- Each green face shares an edge with the white face, and there are **4 edges** connecting the green faces to the white faces.
- Each edge consists of **5 tiny cubes** (since the cube is 5 units long).
Calculating the Unique Cubes
- The cubes at the corners of each edge will have three colors (green, white, and blue) and thus cannot be counted.
- Each edge has **3 inner cubes** that are neither corner cubes, which means they are the only ones that can have one green and one white face.
Final Calculation
- Since there are **4 edges** meeting at the green and white faces, and each edge contributes **3 tiny cubes**, the total number of tiny cubes with one green and one white face is:
\[
4 \text{ edges} \times 3 \text{ cubes/edge} = 12 \text{ tiny cubes}
\]
In conclusion, **the correct number of tiny cubes that will have one portion white and one portion green is 12**, not 18.
Understanding the Cube Structure
- The big cube is segmented into **125 tiny cubes**, indicating it is a **5x5x5 cube** (since \(5^3 = 125\)).
- The cube has **3 different colors**: green, white, and blue.
Color Distribution
- **Green Faces**: Two adjacent faces are painted green.
- **White Faces**: The opposite two faces of the green ones are painted white.
- **Blue Faces**: The remaining two faces are painted blue.
Finding Tiny Cubes with Green and White Faces
- The tiny cubes that have one face green and one face white must be located along the **edges** where the green and white faces meet.
Counting the Relevant Edges
- Each green face shares an edge with the white face, and there are **4 edges** connecting the green faces to the white faces.
- Each edge consists of **5 tiny cubes** (since the cube is 5 units long).
Calculating the Unique Cubes
- The cubes at the corners of each edge will have three colors (green, white, and blue) and thus cannot be counted.
- Each edge has **3 inner cubes** that are neither corner cubes, which means they are the only ones that can have one green and one white face.
Final Calculation
- Since there are **4 edges** meeting at the green and white faces, and each edge contributes **3 tiny cubes**, the total number of tiny cubes with one green and one white face is:
\[
4 \text{ edges} \times 3 \text{ cubes/edge} = 12 \text{ tiny cubes}
\]
In conclusion, **the correct number of tiny cubes that will have one portion white and one portion green is 12**, not 18.
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Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.How many tiny cubes will be formed having one portion white and one portion green for sure?18?
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Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.How many tiny cubes will be formed having one portion white and one portion green for sure?18? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.How many tiny cubes will be formed having one portion white and one portion green for sure?18? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.How many tiny cubes will be formed having one portion white and one portion green for sure?18?.
Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.How many tiny cubes will be formed having one portion white and one portion green for sure?18? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.How many tiny cubes will be formed having one portion white and one portion green for sure?18? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.How many tiny cubes will be formed having one portion white and one portion green for sure?18?.
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