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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?.
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