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4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -
  • a)
    2:1
  • b)
    1:2
  • c)
    1:4
  • d)
    4:1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
4 identical solid spheres are melted and re-formed into a solid hemis...
Let radius of sphere be ‘r’ and radius of hemisphere be ‘R’.
Then, ATQ,
Volume of Spheres = Volume of Hemisphere
4 x (4/3)πr3 = (2/3)πR3
Or, R / r = (8)1/3 = 2 …(1)
C.S.A of hemisphere = 2πR2
And, Surface area of sphere = 4πr2
ATQ,
2πR2 :( ½) of 4πr2
= 2πR2 :2πr2 = R2 :r2 {using (1)}
= 4 :1
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4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer?
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4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer?.
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