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If the radius of a sphere is doubled, then the ratio of the volume of the original sphere to that of the new one is
- a)16 : 1
- b)1: 16
- c)1 : 8
- d)8 : 1
Correct answer is option 'C'. Can you explain this answer?
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Introduction:
In this problem, we are given a sphere and its radius. We need to find the ratio of the volume of the original sphere to the volume of a new sphere when its radius is doubled.
Given:
- Radius of the original sphere = r
Formula:
The formula to calculate the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.
Solution:
To find the ratio of the volumes, we need to calculate the volumes of both spheres and then divide them.
Volume of the original sphere:
The volume of the original sphere is given by V1 = (4/3)πr³.
Volume of the new sphere:
When the radius is doubled, the new radius becomes 2r. Therefore, the volume of the new sphere is given by V2 = (4/3)π(2r)³ = (4/3)π(8r³) = (4/3)π(8)(r³) = (32/3)πr³.
Ratio of the volumes:
Now, we can calculate the ratio of the volumes by dividing the volume of the original sphere by the volume of the new sphere:
Ratio = V1/V2 = [(4/3)πr³] / [(32/3)πr³] = (4/3)πr³ / (32/3)πr³ = 4/32 = 1/8.
Conclusion:
Therefore, the ratio of the volume of the original sphere to that of the new one is 1:8, which corresponds to option C.
In this problem, we are given a sphere and its radius. We need to find the ratio of the volume of the original sphere to the volume of a new sphere when its radius is doubled.
Given:
- Radius of the original sphere = r
Formula:
The formula to calculate the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.
Solution:
To find the ratio of the volumes, we need to calculate the volumes of both spheres and then divide them.
Volume of the original sphere:
The volume of the original sphere is given by V1 = (4/3)πr³.
Volume of the new sphere:
When the radius is doubled, the new radius becomes 2r. Therefore, the volume of the new sphere is given by V2 = (4/3)π(2r)³ = (4/3)π(8r³) = (4/3)π(8)(r³) = (32/3)πr³.
Ratio of the volumes:
Now, we can calculate the ratio of the volumes by dividing the volume of the original sphere by the volume of the new sphere:
Ratio = V1/V2 = [(4/3)πr³] / [(32/3)πr³] = (4/3)πr³ / (32/3)πr³ = 4/32 = 1/8.
Conclusion:
Therefore, the ratio of the volume of the original sphere to that of the new one is 1:8, which corresponds to option C.
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If the radius of a sphere is doubled, then the ratio of the volume of the original sphere to that of the new one isa)16 : 1b)1: 16c)1 : 8d)8 : 1Correct answer is option 'C'. Can you explain this answer?
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If the radius of a sphere is doubled, then the ratio of the volume of the original sphere to that of the new one isa)16 : 1b)1: 16c)1 : 8d)8 : 1Correct answer is option 'C'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the radius of a sphere is doubled, then the ratio of the volume of the original sphere to that of the new one isa)16 : 1b)1: 16c)1 : 8d)8 : 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the radius of a sphere is doubled, then the ratio of the volume of the original sphere to that of the new one isa)16 : 1b)1: 16c)1 : 8d)8 : 1Correct answer is option 'C'. Can you explain this answer?.
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