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The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is
- a)64 : 27
- b)16 : 9
- c)16 : 27
- d)27 : 64
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The surface areas of two spheres are in the ratio 16 : 9. The ratio of...
Let r1 and r2 be the radius of the two spheres respectively. Therefore. the ratio of their volumes.
Now, ratio of thier volumes,
Now, ratio of thier volumes,
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The surface areas of two spheres are in the ratio 16 : 9. The ratio of...
Let the radii of spheres be a and b
According to question,
A1 / A2 = 16/9
=> 4 pi a^2 / 4 pi b^2 = 16 / 9
=> a^2 / b^2 = 16 / 9
=> a/b = 4/3
Now,
V1 / V2 = 4/3 pi a^3 / 4/3 pi b^3
=> V1 / V2 = a^3 / b^3
=> V1 / V2 = (4 /3)^3
=> V1 / V2 = 64/ 27
=> V1 : V2 = 64 : 27.
According to question,
A1 / A2 = 16/9
=> 4 pi a^2 / 4 pi b^2 = 16 / 9
=> a^2 / b^2 = 16 / 9
=> a/b = 4/3
Now,
V1 / V2 = 4/3 pi a^3 / 4/3 pi b^3
=> V1 / V2 = a^3 / b^3
=> V1 / V2 = (4 /3)^3
=> V1 / V2 = 64/ 27
=> V1 : V2 = 64 : 27.
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The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes isa)64 : 27b)16 : 9c)16 : 27d)27 : 64Correct answer is option 'A'. Can you explain this answer?
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The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes isa)64 : 27b)16 : 9c)16 : 27d)27 : 64Correct answer is option 'A'. 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 The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes isa)64 : 27b)16 : 9c)16 : 27d)27 : 64Correct answer is option 'A'. 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 The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes isa)64 : 27b)16 : 9c)16 : 27d)27 : 64Correct answer is option 'A'. Can you explain this answer?.
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