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A cube of side 10cm is coloured green with a 2 cm wide red strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size then how many cubes are without any colour?
- a)4
- b)8
- c)27
- d)64
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A cube of side 10cm is coloured green with a 2 cm wide red strip along...
Understanding the Cube Dimensions
The original cube has a side length of 10 cm. It is painted with a 2 cm wide red strip along all edges of each face.
Calculating the Inner Dimension
- The red strip removes 2 cm from each side of the cube.
- Since the strip is painted on all sides, we need to subtract 4 cm (2 cm from each side) from the original dimension.
- Thus, the dimension of the unpainted inner cube is:
- 10 cm - 4 cm = 6 cm.
Volume of the Smaller Cubes
- The cube is divided into 125 smaller cubes.
- Since 125 is equal to 5^3, each smaller cube has a side length of:
- 10 cm / 5 = 2 cm.
Determining the Number of Unpainted Cubes
- The unpainted inner cube has dimensions of 6 cm, and since each smaller cube has a side of 2 cm, we can determine how many smaller cubes fit within the unpainted area:
- Number of smaller cubes along each dimension = 6 cm / 2 cm = 3 cubes.
- Therefore, the total number of smaller cubes that are completely unpainted is:
- 3 x 3 x 3 = 27.
Conclusion
The total number of smaller cubes without any color is 27. Thus, the correct answer is option C.
The original cube has a side length of 10 cm. It is painted with a 2 cm wide red strip along all edges of each face.
Calculating the Inner Dimension
- The red strip removes 2 cm from each side of the cube.
- Since the strip is painted on all sides, we need to subtract 4 cm (2 cm from each side) from the original dimension.
- Thus, the dimension of the unpainted inner cube is:
- 10 cm - 4 cm = 6 cm.
Volume of the Smaller Cubes
- The cube is divided into 125 smaller cubes.
- Since 125 is equal to 5^3, each smaller cube has a side length of:
- 10 cm / 5 = 2 cm.
Determining the Number of Unpainted Cubes
- The unpainted inner cube has dimensions of 6 cm, and since each smaller cube has a side of 2 cm, we can determine how many smaller cubes fit within the unpainted area:
- Number of smaller cubes along each dimension = 6 cm / 2 cm = 3 cubes.
- Therefore, the total number of smaller cubes that are completely unpainted is:
- 3 x 3 x 3 = 27.
Conclusion
The total number of smaller cubes without any color is 27. Thus, the correct answer is option C.
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Community Answer
A cube of side 10cm is coloured green with a 2 cm wide red strip along...
There are 9 central cubes in three middle layers, which are without any colour.
∴ No. of cubes without any colour = 9 × 3 = 27
∴ No. of cubes without any colour = 9 × 3 = 27
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A cube of side 10cm is coloured green with a 2 cm wide red strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size then how many cubes are without any colour?a)4b)8c)27d)64Correct answer is option 'C'. Can you explain this answer?
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A cube of side 10cm is coloured green with a 2 cm wide red strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size then how many cubes are without any colour?a)4b)8c)27d)64Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A cube of side 10cm is coloured green with a 2 cm wide red strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size then how many cubes are without any colour?a)4b)8c)27d)64Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube of side 10cm is coloured green with a 2 cm wide red strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size then how many cubes are without any colour?a)4b)8c)27d)64Correct answer is option 'C'. Can you explain this answer?.
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