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The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :
- a)14400 cm2
- b)44200 cm2
- c)57600 cm2
- d)86400 cm2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The dimensions of a piece of iron in the shape of a cuboid are 270 cm...
Volume of cube = volume of cuboid
= 270 x 100 x 64 = 1728000 cm3
∴ Length of one side of the cube = 120 cm
∴ Surface area of cube = 6 x 120 x 120 = 86400 cm2
Most Upvoted Answer
The dimensions of a piece of iron in the shape of a cuboid are 270 cm...
To find the surface area of the cube, we need to know the length of its sides.
Given:
Dimensions of the original cuboid: 270 cm x 100 cm x 64 cm
Step 1: Find the volume of the original cuboid
The volume of a cuboid is given by the formula: Volume = length x width x height.
So, the volume of the original cuboid = 270 cm x 100 cm x 64 cm = 1,728,000 cm³.
Step 2: Find the side length of the cube
Since the original cuboid is melted and recast into a cube, the volume of the cube will be the same as the volume of the original cuboid.
So, the volume of the cube = 1,728,000 cm³.
The volume of a cube is given by the formula: Volume = side³.
Therefore, 1,728,000 cm³ = side³.
Step 3: Find the side length of the cube by finding the cubic root of the volume
Taking the cubic root of both sides, we get:
side = ∛(1,728,000 cm³).
Calculating the cubic root of 1,728,000 cm³, we find:
side ≈ 120 cm.
Step 4: Find the surface area of the cube
The surface area of a cube is given by the formula: Surface Area = 6 x side².
Substituting the value of the side, we get:
Surface Area = 6 x (120 cm)² = 6 x 14,400 cm² = 86,400 cm².
Therefore, the surface area of the cube is 86,400 cm².
Thus, the correct answer is option 'D' (86,400 cm²).
Given:
Dimensions of the original cuboid: 270 cm x 100 cm x 64 cm
Step 1: Find the volume of the original cuboid
The volume of a cuboid is given by the formula: Volume = length x width x height.
So, the volume of the original cuboid = 270 cm x 100 cm x 64 cm = 1,728,000 cm³.
Step 2: Find the side length of the cube
Since the original cuboid is melted and recast into a cube, the volume of the cube will be the same as the volume of the original cuboid.
So, the volume of the cube = 1,728,000 cm³.
The volume of a cube is given by the formula: Volume = side³.
Therefore, 1,728,000 cm³ = side³.
Step 3: Find the side length of the cube by finding the cubic root of the volume
Taking the cubic root of both sides, we get:
side = ∛(1,728,000 cm³).
Calculating the cubic root of 1,728,000 cm³, we find:
side ≈ 120 cm.
Step 4: Find the surface area of the cube
The surface area of a cube is given by the formula: Surface Area = 6 x side².
Substituting the value of the side, we get:
Surface Area = 6 x (120 cm)² = 6 x 14,400 cm² = 86,400 cm².
Therefore, the surface area of the cube is 86,400 cm².
Thus, the correct answer is option 'D' (86,400 cm²).
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The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :a)14400 cm2b)44200 cm2c)57600 cm2d)86400 cm2Correct answer is option 'D'. Can you explain this answer?
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The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :a)14400 cm2b)44200 cm2c)57600 cm2d)86400 cm2Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :a)14400 cm2b)44200 cm2c)57600 cm2d)86400 cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :a)14400 cm2b)44200 cm2c)57600 cm2d)86400 cm2Correct answer is option 'D'. Can you explain this answer?.
The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :a)14400 cm2b)44200 cm2c)57600 cm2d)86400 cm2Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :a)14400 cm2b)44200 cm2c)57600 cm2d)86400 cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be :a)14400 cm2b)44200 cm2c)57600 cm2d)86400 cm2Correct answer is option 'D'. Can you explain this answer?.
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