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If a spherical balloon grows to twice its radius when inflated, then the ratio of the volume of the inflated balloon to the original balloon is
- a)it is 8 : 1
- b)it is 4 : 1
- c)it is 5 : 1
- d)it is 6 : 1
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If a spherical balloon grows to twice its radius when inflated, then t...
Volume of spherical balloon before inflating-4/3πr³,
Volume of spherical balloon after inflating-4/3π(2r)³
Ratio of volume of infalte balloon to original
=4/3π(2r)³/4/3πr³
=2r³/r³=(2)³(r)³/(r)³
=2³/1
=8/1=8:1, so option 'A' is correct
Volume of spherical balloon after inflating-4/3π(2r)³
Ratio of volume of infalte balloon to original
=4/3π(2r)³/4/3πr³
=2r³/r³=(2)³(r)³/(r)³
=2³/1
=8/1=8:1, so option 'A' is correct
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Community Answer
If a spherical balloon grows to twice its radius when inflated, then t...
Hypothesis:
Let the original radius of the balloon be 'r'.
When the balloon is inflated, its radius becomes '2r'.
Calculating the Volume:
The volume of a sphere is given by the formula:
V = (4/3)πr^3
Calculating the Volume of the Original Balloon:
Substituting the original radius 'r' into the volume formula, we get:
V1 = (4/3)πr^3
Calculating the Volume of the Inflated Balloon:
Substituting the inflated radius '2r' into the volume formula, we get:
V2 = (4/3)π(2r)^3
= (4/3)π8r^3
= (32/3)πr^3
Finding the Ratio:
The ratio of the volume of the inflated balloon to the original balloon can be calculated by dividing the volume of the inflated balloon by the volume of the original balloon:
Ratio = V2/V1
= [(32/3)πr^3] / [(4/3)πr^3]
= (32/3) / (4/3)
= 32/4
= 8
Conclusion:
Therefore, the ratio of the volume of the inflated balloon to the original balloon is 8:1.
Let the original radius of the balloon be 'r'.
When the balloon is inflated, its radius becomes '2r'.
Calculating the Volume:
The volume of a sphere is given by the formula:
V = (4/3)πr^3
Calculating the Volume of the Original Balloon:
Substituting the original radius 'r' into the volume formula, we get:
V1 = (4/3)πr^3
Calculating the Volume of the Inflated Balloon:
Substituting the inflated radius '2r' into the volume formula, we get:
V2 = (4/3)π(2r)^3
= (4/3)π8r^3
= (32/3)πr^3
Finding the Ratio:
The ratio of the volume of the inflated balloon to the original balloon can be calculated by dividing the volume of the inflated balloon by the volume of the original balloon:
Ratio = V2/V1
= [(32/3)πr^3] / [(4/3)πr^3]
= (32/3) / (4/3)
= 32/4
= 8
Conclusion:
Therefore, the ratio of the volume of the inflated balloon to the original balloon is 8:1.
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If a spherical balloon grows to twice its radius when inflated, then the ratio of the volume of the inflated balloon to the original balloon isa)it is 8 : 1b)it is 4 : 1c)it is 5 : 1d)it is 6 : 1Correct answer is option 'A'. Can you explain this answer?
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If a spherical balloon grows to twice its radius when inflated, then the ratio of the volume of the inflated balloon to the original balloon isa)it is 8 : 1b)it is 4 : 1c)it is 5 : 1d)it is 6 : 1Correct answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If a spherical balloon grows to twice its radius when inflated, then the ratio of the volume of the inflated balloon to the original balloon isa)it is 8 : 1b)it is 4 : 1c)it is 5 : 1d)it is 6 : 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a spherical balloon grows to twice its radius when inflated, then the ratio of the volume of the inflated balloon to the original balloon isa)it is 8 : 1b)it is 4 : 1c)it is 5 : 1d)it is 6 : 1Correct answer is option 'A'. Can you explain this answer?.
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