Directions: A spherical ball of radius R is cut into 2 halves. There is a cylindrical rod of height h, which is 8 times its radius r. The two cut hemispheres are attached at the two ends of the rod.The spheres cover half the length while half length remains open. The complete rod is coveredwith a paper leaving the top and bottom of the rod. Further to cover the portion of the rod notcovered by the hemispheres, the same paper is used but this time the covering has a radius R.What is the ratio of the area of paper used to cover the rod to the area of paper used to cover the open portion of the rod?a)1 : √5b)2 : √5c)1 : 5√5d)5 : √5Correct answer is option 'B'. Can you explain this answer?

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Directions: A spherical ball of radius R is cut into 2 halves. There is a cylindrical rod of height h, which is 8 times its radius r. The two cut hemispheres are attached at the two ends of the rod.

The spheres cover half the length while half length remains open. The complete rod is covered

with a paper leaving the top and bottom of the rod. Further to cover the portion of the rod not

covered by the hemispheres, the same paper is used but this time the covering has a radius R.

What is the ratio of the area of paper used to cover the rod to the area of paper used to cover the open portion of the rod?

a)
1 : √5
b)
2 : √5
c)
1 : 5√5
d)
5 : √5

Correct answer is option 'B'. Can you explain this answer?

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Most Upvoted Answer

Directions: A spherical ball of radius R is cut into 2 halves. There i...

Let h be the height of the rod and r be the radius. h = 8r. Let R be the radius of the sphere cut. The figure looks like -

r² + 4r² = R

R = √5r

The area of the covering is the surface area of the rod and the cylindrical covering as shown

above

Surface area of rod = 2prh = 2pr.8r = 16pr²

Area of sheet used to cover open portion with radius R

=8√5 pr²

Ratio of the area of paper used to cover the rod to the area of paper used to cover the open

portion of the rod = 16pr² :8√5pr²

= 2 : √5.

Hence, the correct option is (b).

Answered by Wizius Careers · View profile

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Directions: A spherical ball of radius R is cut into 2 halves. There is a cylindrical rod of height h, which is 8 times its radius r. The two cut hemispheres are attached at the two ends of the rod.The spheres cover half the length while half length remains open. The complete rod is coveredwith a paper leaving the top and bottom of the rod. Further to cover the portion of the rod notcovered by the hemispheres, the same paper is used but this time the covering has a radius R.What is the ratio of the area of paper used to cover the rod to the area of paper used to cover the open portion of the rod?a)1 : √5b)2 : √5c)1 : 5√5d)5 : √5Correct answer is option 'B'. Can you explain this answer?

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Directions: A spherical ball of radius R is cut into 2 halves. There is a cylindrical rod of height h, which is 8 times its radius r. The two cut hemispheres are attached at the two ends of the rod.The spheres cover half the length while half length remains open. The complete rod is coveredwith a paper leaving the top and bottom of the rod. Further to cover the portion of the rod notcovered by the hemispheres, the same paper is used but this time the covering has a radius R.What is the ratio of the area of paper used to cover the rod to the area of paper used to cover the open portion of the rod?a)1 : √5b)2 : √5c)1 : 5√5d)5 : √5Correct answer is option 'B'. 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 Directions: A spherical ball of radius R is cut into 2 halves. There is a cylindrical rod of height h, which is 8 times its radius r. The two cut hemispheres are attached at the two ends of the rod.The spheres cover half the length while half length remains open. The complete rod is coveredwith a paper leaving the top and bottom of the rod. Further to cover the portion of the rod notcovered by the hemispheres, the same paper is used but this time the covering has a radius R.What is the ratio of the area of paper used to cover the rod to the area of paper used to cover the open portion of the rod?a)1 : √5b)2 : √5c)1 : 5√5d)5 : √5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: A spherical ball of radius R is cut into 2 halves. There is a cylindrical rod of height h, which is 8 times its radius r. The two cut hemispheres are attached at the two ends of the rod.The spheres cover half the length while half length remains open. The complete rod is coveredwith a paper leaving the top and bottom of the rod. Further to cover the portion of the rod notcovered by the hemispheres, the same paper is used but this time the covering has a radius R.What is the ratio of the area of paper used to cover the rod to the area of paper used to cover the open portion of the rod?a)1 : √5b)2 : √5c)1 : 5√5d)5 : √5Correct answer is option 'B'. Can you explain this answer?.

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