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A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?
- a)6027 cm2
- b)5034 cm2
- c)6084 cm2
- d)5097 cm2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A wooden cylinder of radius 21 cm and height 28 cm is cut into four id...
The sum of the surface areas of BFEC and BCDA (which are rectangles)
► = 2 x BF x BC = 2 x 21 cm x 28 cm = 1176 cm2 ..........(1)
Total area of the flat surfaces (circular bottom and top) = 2[3 / 4 x (21)2] cm2
► = 2 x 3 / 4 x 22 / 7 x 21 x 21 cm2 = 2079 cm2 ..........(2)
► = 2 x 3 / 4 x 22 / 7 x 21 x 21 cm2 = 2079 cm2 ..........(2)
Area of the curved surface = 3 / 4 x 2 x 21 x 28 cm2
► = 3 / 4 x 2 x 22 / 7 x 21 x 28 cm2 = 2772 cm2 ..........(3)
► = 3 / 4 x 2 x 22 / 7 x 21 x 28 cm2 = 2772 cm2 ..........(3)
So, total surface area of the new block after adding (1), (2) and (3)
► = (1176 + 2079 + 2772) cm2 = 6027 cm2.
► = (1176 + 2079 + 2772) cm2 = 6027 cm2.
Most Upvoted Answer
A wooden cylinder of radius 21 cm and height 28 cm is cut into four id...
Given:
- Radius of the wooden cylinder = 21 cm
- Height of the wooden cylinder = 28 cm
To find:
- The total surface area of the resulting wooden block after three pieces are joined back together.
Solution:
1. Volume of the wooden cylinder:
- The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
- Substituting the given values, we have V = π(21^2)(28) = 21^2(22/7)(28) = 12348 cm^3.
2. Volume of each piece:
- The wooden cylinder is cut into four identical pieces.
- Therefore, the volume of each piece is 12348/4 = 3087 cm^3.
3. Surface area of each piece:
- Let's consider one of the pieces after cutting the cylinder.
- The shape of the piece is a curved surface of a cylinder along with two circular bases.
- The curved surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height.
- Substituting the given values, we have A = 2(22/7)(21)(28) = 3696 cm^2.
- The area of each circular base is πr^2 = (22/7)(21^2) = 1386 cm^2.
- Therefore, the total surface area of each piece is 3696 + 2(1386) = 6468 cm^2.
4. Surface area of the resulting wooden block:
- After three pieces are joined back together, we have a wooden block with the volume of three pieces.
- The volume of the resulting wooden block is 3(3087) = 9261 cm^3.
- The surface area of the resulting wooden block is the same as the surface area of three pieces.
- Therefore, the total surface area of the resulting wooden block is 3(6468) = 19404 cm^2.
Hence, the correct answer is option A) 6027 cm^2.
- Radius of the wooden cylinder = 21 cm
- Height of the wooden cylinder = 28 cm
To find:
- The total surface area of the resulting wooden block after three pieces are joined back together.
Solution:
1. Volume of the wooden cylinder:
- The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
- Substituting the given values, we have V = π(21^2)(28) = 21^2(22/7)(28) = 12348 cm^3.
2. Volume of each piece:
- The wooden cylinder is cut into four identical pieces.
- Therefore, the volume of each piece is 12348/4 = 3087 cm^3.
3. Surface area of each piece:
- Let's consider one of the pieces after cutting the cylinder.
- The shape of the piece is a curved surface of a cylinder along with two circular bases.
- The curved surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height.
- Substituting the given values, we have A = 2(22/7)(21)(28) = 3696 cm^2.
- The area of each circular base is πr^2 = (22/7)(21^2) = 1386 cm^2.
- Therefore, the total surface area of each piece is 3696 + 2(1386) = 6468 cm^2.
4. Surface area of the resulting wooden block:
- After three pieces are joined back together, we have a wooden block with the volume of three pieces.
- The volume of the resulting wooden block is 3(3087) = 9261 cm^3.
- The surface area of the resulting wooden block is the same as the surface area of three pieces.
- Therefore, the total surface area of the resulting wooden block is 3(6468) = 19404 cm^2.
Hence, the correct answer is option A) 6027 cm^2.
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A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer?
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A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer?.
A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer?.
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A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A wooden cylinder of radius 21 cm and height 28 cm is cut into four identical pieces by making two cuts perpendicular to its base. If three of the four pieces are again joined back together in their original position, then what is the total surface area ( sq.cm) of this resulting wooden block ?a)6027 cm2b)5034 cm2c)6084 cm2d)5097 cm2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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