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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 volume of rod not covered by the sphere to the volume of sphere not covered by the rod?
  • a)
    1 : 5 : √5
  • b)
    5-√5-1 : 1
  • c)
    3 : 5-√5-3
  • d)
    5 : √5-1
Correct answer is option 'C'. Can you explain this answer?
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 = R2
R = √5r
Volume of Rod not covered by the spheres = pr2h = pr2.4r = 4pr3
Volume of Sphere not covered by the Rod =
Ratio of the volume of rod not covered by the sphere to the volume of sphere not covered by the rod = 3 : (5√5 - 3).
Hence, the correct option is (c).
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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 volume of rod not covered by the sphere to the volume of sphere not covered by the rod?a)1 : 5 : √5b)5-√5-1 : 1c)3 : 5-√5-3d)5 : √5-1Correct answer is option 'C'. 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 volume of rod not covered by the sphere to the volume of sphere not covered by the rod?a)1 : 5 : √5b)5-√5-1 : 1c)3 : 5-√5-3d)5 : √5-1Correct answer is option 'C'. 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 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 volume of rod not covered by the sphere to the volume of sphere not covered by the rod?a)1 : 5 : √5b)5-√5-1 : 1c)3 : 5-√5-3d)5 : √5-1Correct answer is option 'C'. 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 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 volume of rod not covered by the sphere to the volume of sphere not covered by the rod?a)1 : 5 : √5b)5-√5-1 : 1c)3 : 5-√5-3d)5 : √5-1Correct answer is option 'C'. Can you explain this answer?.
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