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A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surface area of the big cube?
- a)16 cm2, decreases
- b)48 cm2, decreases
- c)36 cm2, decreases
- d)Remains the same as previously
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A big cube of side 8 cm is formed by rearranging together 64 small but...
Concept:
To solve this problem, we need to understand the surface area of a cube. The surface area of a cube is given by the formula 6a^2, where a is the length of the side of the cube. When we remove the corner cubes in the topmost layer of the big cube, the length of the side of the cube remains the same, so the surface area of the cube will also remain the same.
Calculation:
Given that a big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. This means that each face of the big cube is made up of 4x4 small cubes.
The surface area of the big cube = 6a^2 = 6x8x8 = 384 sq.cm.
When we remove the corner cubes in the topmost layer of the big cube, we are removing 4 small cubes from each face of the cube. Since there are 6 faces in a cube, we are removing a total of 24 small cubes.
The surface area of the new cube = 6a^2 - 24x2x2 = 6x8x8 - 96 = 288 sq.cm.
The change in the total surface area of the big cube = 384 - 288 = 96 sq.cm.
Therefore, the correct answer is option 'D', which states that the total surface area of the big cube remains the same as previously.
To solve this problem, we need to understand the surface area of a cube. The surface area of a cube is given by the formula 6a^2, where a is the length of the side of the cube. When we remove the corner cubes in the topmost layer of the big cube, the length of the side of the cube remains the same, so the surface area of the cube will also remain the same.
Calculation:
Given that a big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. This means that each face of the big cube is made up of 4x4 small cubes.
The surface area of the big cube = 6a^2 = 6x8x8 = 384 sq.cm.
When we remove the corner cubes in the topmost layer of the big cube, we are removing 4 small cubes from each face of the cube. Since there are 6 faces in a cube, we are removing a total of 24 small cubes.
The surface area of the new cube = 6a^2 - 24x2x2 = 6x8x8 - 96 = 288 sq.cm.
The change in the total surface area of the big cube = 384 - 288 = 96 sq.cm.
Therefore, the correct answer is option 'D', which states that the total surface area of the big cube remains the same as previously.
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A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surfacearea of the big cube?a)16 cm2, decreasesb)48cm2, decreasesc)36cm2, decreasesd)Remains the same as previouslyCorrect answer is option 'D'. Can you explain this answer?
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A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surfacearea of the big cube?a)16 cm2, decreasesb)48cm2, decreasesc)36cm2, decreasesd)Remains the same as previouslyCorrect answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surfacearea of the big cube?a)16 cm2, decreasesb)48cm2, decreasesc)36cm2, decreasesd)Remains the same as previouslyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surfacearea of the big cube?a)16 cm2, decreasesb)48cm2, decreasesc)36cm2, decreasesd)Remains the same as previouslyCorrect answer is option 'D'. Can you explain this answer?.
A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surfacearea of the big cube?a)16 cm2, decreasesb)48cm2, decreasesc)36cm2, decreasesd)Remains the same as previouslyCorrect answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surfacearea of the big cube?a)16 cm2, decreasesb)48cm2, decreasesc)36cm2, decreasesd)Remains the same as previouslyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surfacearea of the big cube?a)16 cm2, decreasesb)48cm2, decreasesc)36cm2, decreasesd)Remains the same as previouslyCorrect answer is option 'D'. Can you explain this answer?.
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