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Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere. The volume of the new sphere is
- a)118884 cm3
- b)116444 cm3
- c)116424 cm3
- d)116664 cm3
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Six hemispherical bowls each of radius 21 cm are melted and recasted i...
Ans:- let radius of spheres be
r1=r2=r3=r4=r5=r6=21cm.
Volume of one hemispherical bowl
= 2/3πr3
=2/3×22/7×21×21×21.
=2×22×7×3×21.
=44×441
=19404 cm3.
Therefore,
Volume of 6 hemispherical bowls.
=Volume of 1 hemispherical bowl × 6
=19404 cm3 × 6
=116424cm3.
Here,
Volume of 6 hemispherical bowl = Volume of new sphere.
therefore,
Volume of new sphere= 116424cm3.
r1=r2=r3=r4=r5=r6=21cm.
Volume of one hemispherical bowl
= 2/3πr3
=2/3×22/7×21×21×21.
=2×22×7×3×21.
=44×441
=19404 cm3.
Therefore,
Volume of 6 hemispherical bowls.
=Volume of 1 hemispherical bowl × 6
=19404 cm3 × 6
=116424cm3.
Here,
Volume of 6 hemispherical bowl = Volume of new sphere.
therefore,
Volume of new sphere= 116424cm3.
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Six hemispherical bowls each of radius 21 cm are melted and recasted i...
Given information:
- Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere.
To find:
- The volume of the new sphere.
Solution:
1. Volume of a hemisphere:
- The formula to calculate the volume of a hemisphere is given by: V = (2/3)πr³, where r is the radius of the hemisphere.
- Since we have six hemispheres, we can find the total volume of all six hemispheres.
2. Total volume of six hemispheres:
- Given that the radius of each hemisphere is 21 cm, we can substitute this value into the formula to find the volume of one hemisphere.
- V₁ = (2/3)π(21)³
- V₁ = (2/3)π(9261)
- V₁ = (18522/3)π
- V₁ = 6174π cm³ (approx)
- Since there are six hemispheres, the total volume of all six hemispheres is:
- V = 6 * V₁
- V = 6 * 6174π
- V = 37044π cm³ (approx)
3. Volume of the new sphere:
- The volume of a sphere is given by the formula: V = (4/3)πr³, where r is the radius of the sphere.
- The new sphere is made by melting and recasting the six hemispheres, so its volume is equal to the total volume of all six hemispheres.
- Therefore, the volume of the new sphere is: V = 37044π cm³ (approx)
Answer:
- The volume of the new sphere is approximately 37044π cm³.
- In decimal form, the volume is approximately 116424 cm³.
- Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere.
To find:
- The volume of the new sphere.
Solution:
1. Volume of a hemisphere:
- The formula to calculate the volume of a hemisphere is given by: V = (2/3)πr³, where r is the radius of the hemisphere.
- Since we have six hemispheres, we can find the total volume of all six hemispheres.
2. Total volume of six hemispheres:
- Given that the radius of each hemisphere is 21 cm, we can substitute this value into the formula to find the volume of one hemisphere.
- V₁ = (2/3)π(21)³
- V₁ = (2/3)π(9261)
- V₁ = (18522/3)π
- V₁ = 6174π cm³ (approx)
- Since there are six hemispheres, the total volume of all six hemispheres is:
- V = 6 * V₁
- V = 6 * 6174π
- V = 37044π cm³ (approx)
3. Volume of the new sphere:
- The volume of a sphere is given by the formula: V = (4/3)πr³, where r is the radius of the sphere.
- The new sphere is made by melting and recasting the six hemispheres, so its volume is equal to the total volume of all six hemispheres.
- Therefore, the volume of the new sphere is: V = 37044π cm³ (approx)
Answer:
- The volume of the new sphere is approximately 37044π cm³.
- In decimal form, the volume is approximately 116424 cm³.
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Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere. The volume of the new sphere isa)118884 cm3b)116444 cm3c)116424 cm3d)116664 cm3Correct answer is option 'C'. Can you explain this answer?
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Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere. The volume of the new sphere isa)118884 cm3b)116444 cm3c)116424 cm3d)116664 cm3Correct answer is option 'C'. 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 Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere. The volume of the new sphere isa)118884 cm3b)116444 cm3c)116424 cm3d)116664 cm3Correct answer is option 'C'. 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 Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere. The volume of the new sphere isa)118884 cm3b)116444 cm3c)116424 cm3d)116664 cm3Correct answer is option 'C'. Can you explain this answer?.
Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere. The volume of the new sphere isa)118884 cm3b)116444 cm3c)116424 cm3d)116664 cm3Correct answer is option 'C'. 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 Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere. The volume of the new sphere isa)118884 cm3b)116444 cm3c)116424 cm3d)116664 cm3Correct answer is option 'C'. 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 Six hemispherical bowls each of radius 21 cm are melted and recasted into a sphere. The volume of the new sphere isa)118884 cm3b)116444 cm3c)116424 cm3d)116664 cm3Correct answer is option 'C'. Can you explain this answer?.
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