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If the surface areas of two spheres are in the ratio 4 : 9, then the ratio of their volumes is :
  • a)
    8 : 25
  • b)
    8 : 26
  • c)
    8 : 27
  • d)
    8 : 28
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the surface areas of two spheres are in the ratio 4 : 9, then the r...
Let r and R are two radius of a spheres.


According to the question,

⇒  4πR24πr2​=94​


⇒  R2r2​=64​


Taking square root on both sides.

⇒  Rr​=32​         ---- ( 1 )


The volume of two spheres are in ratio,

⇒  34​πR334​πr3​


⇒  R3r3​


From ( 1 ),


⇒  (3)3(2)3​

⇒  278​

∴  The required ratio is 8:27
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If the surface areas of two spheres are in the ratio 4 : 9, then the ratio of their volumes is :a)8 : 25b)8 : 26c)8 : 27d)8 : 28Correct answer is option 'C'. Can you explain this answer?
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If the surface areas of two spheres are in the ratio 4 : 9, then the ratio of their volumes is :a)8 : 25b)8 : 26c)8 : 27d)8 : 28Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the surface areas of two spheres are in the ratio 4 : 9, then the ratio of their volumes is :a)8 : 25b)8 : 26c)8 : 27d)8 : 28Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the surface areas of two spheres are in the ratio 4 : 9, then the ratio of their volumes is :a)8 : 25b)8 : 26c)8 : 27d)8 : 28Correct answer is option 'C'. Can you explain this answer?.
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