Railways Exam > Railways Questions > The dimensions of a piece of iron in the sha...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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...
Given:
Dimensions of the cuboid: 270 cm x 100 cm x 64 cm
To find:
Surface area of the cube after melting and recasting
Solution:
To find the surface area of the cube, we need to determine the length of each side of the cube.
Step 1: Volume of the cuboid
The volume of the cuboid can be calculated using the formula:
Volume = Length x Width x Height
Given:
Length = 270 cm
Width = 100 cm
Height = 64 cm
Volume = 270 cm x 100 cm x 64 cm
= 1,728,000 cm³
Step 2: Side length of the cube
Since the cuboid is melted and recast into a cube, the volume of the cube will be equal to the volume of the cuboid.
Given:
Volume of the cube = Volume of the cuboid = 1,728,000 cm³
Let's assume the side length of the cube to be 'a'.
Volume of the cube = a³
Therefore, a³ = 1,728,000 cm³
To find the side length 'a', we need to find the cube root of 1,728,000.
Using a cube root calculator or simplifying manually,
a ≈ 120 cm
Step 3: Surface area of the cube
The surface area of a cube can be calculated using the formula:
Surface Area = 6a²
Given:
Side length of the cube, a = 120 cm
Surface Area = 6 x (120 cm)²
= 6 x 14,400 cm²
= 86,400 cm²
Therefore, the surface area of the cube, after melting and recasting the cuboid, is 86,400 cm².
Answer:
The correct option is (d) 86,400 cm².
Dimensions of the cuboid: 270 cm x 100 cm x 64 cm
To find:
Surface area of the cube after melting and recasting
Solution:
To find the surface area of the cube, we need to determine the length of each side of the cube.
Step 1: Volume of the cuboid
The volume of the cuboid can be calculated using the formula:
Volume = Length x Width x Height
Given:
Length = 270 cm
Width = 100 cm
Height = 64 cm
Volume = 270 cm x 100 cm x 64 cm
= 1,728,000 cm³
Step 2: Side length of the cube
Since the cuboid is melted and recast into a cube, the volume of the cube will be equal to the volume of the cuboid.
Given:
Volume of the cube = Volume of the cuboid = 1,728,000 cm³
Let's assume the side length of the cube to be 'a'.
Volume of the cube = a³
Therefore, a³ = 1,728,000 cm³
To find the side length 'a', we need to find the cube root of 1,728,000.
Using a cube root calculator or simplifying manually,
a ≈ 120 cm
Step 3: Surface area of the cube
The surface area of a cube can be calculated using the formula:
Surface Area = 6a²
Given:
Side length of the cube, a = 120 cm
Surface Area = 6 x (120 cm)²
= 6 x 14,400 cm²
= 86,400 cm²
Therefore, the surface area of the cube, after melting and recasting the cuboid, is 86,400 cm².
Answer:
The correct option is (d) 86,400 cm².
Attention Railways Students!
To make sure you are not studying endlessly, EduRev has designed Railways study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Railways.
|
Explore Courses for Railways exam
|
|
Similar Railways Doubts
Top Courses for RailwaysView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Railways.
Download more important topics, notes, lectures and mock test series for Railways Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Railways tests.
|
|
Explore Courses for Railways exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup