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The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.
- a)3.2 cm
- b)1.6 cm
- c)2.56 cm
- d)5.6 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm...
Let the radius of sphere = R cm
Volume of cone =
× (radius of base of right circular cone)2 × (height of cone)
Volume of the sphere = Volume of the two cones
R3 = (1.6 × 1.6 × 6.4)/4
R3 = 4.096
R = 1.6 cm
Hence, diameter = 2R = 2 x 1.6 = 3.2 cm
Volume of cone =
× (radius of base of right circular cone)2 × (height of cone)Volume of the sphere = Volume of the two cones
R3 = (1.6 × 1.6 × 6.4)/4
R3 = 4.096
R = 1.6 cm
Hence, diameter = 2R = 2 x 1.6 = 3.2 cm
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The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm...
Given data:
- Heights of the two metallic cones: 4.3 cm and 2.1 cm
- Radius of the bases of the cones: 1.6 cm each
Finding the volume of the two cones:
- Volume of a cone = 1/3 * π * r^2 * h
- Volume of the first cone = 1/3 * π * 1.6^2 * 4.3 = 11.419 cm^3
- Volume of the second cone = 1/3 * π * 1.6^2 * 2.1 = 3.747 cm^3
- Total volume of the two cones = 11.419 + 3.747 = 15.166 cm^3
Calculating the radius of the sphere:
- Volume of a sphere = 4/3 * π * r^3
- 4/3 * π * r^3 = 15.166
- r^3 = 15.166 * 3 / 4π
- r^3 ≈ 5.73
- r ≈ 1.8 cm
Calculating the diameter of the sphere:
- Diameter of the sphere = 2 * radius ≈ 2 * 1.8 ≈ 3.6 cm
Therefore, the diameter of the sphere after melting and recasting the two cones together is approximately 3.6 cm, which is closest to option A (3.2 cm).
- Heights of the two metallic cones: 4.3 cm and 2.1 cm
- Radius of the bases of the cones: 1.6 cm each
Finding the volume of the two cones:
- Volume of a cone = 1/3 * π * r^2 * h
- Volume of the first cone = 1/3 * π * 1.6^2 * 4.3 = 11.419 cm^3
- Volume of the second cone = 1/3 * π * 1.6^2 * 2.1 = 3.747 cm^3
- Total volume of the two cones = 11.419 + 3.747 = 15.166 cm^3
Calculating the radius of the sphere:
- Volume of a sphere = 4/3 * π * r^3
- 4/3 * π * r^3 = 15.166
- r^3 = 15.166 * 3 / 4π
- r^3 ≈ 5.73
- r ≈ 1.8 cm
Calculating the diameter of the sphere:
- Diameter of the sphere = 2 * radius ≈ 2 * 1.8 ≈ 3.6 cm
Therefore, the diameter of the sphere after melting and recasting the two cones together is approximately 3.6 cm, which is closest to option A (3.2 cm).
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The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.a)3.2 cmb)1.6 cmc)2.56 cmd)5.6 cmCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.a)3.2 cmb)1.6 cmc)2.56 cmd)5.6 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.a)3.2 cmb)1.6 cmc)2.56 cmd)5.6 cmCorrect answer is option 'A'. Can you explain this answer?.
The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.a)3.2 cmb)1.6 cmc)2.56 cmd)5.6 cmCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.a)3.2 cmb)1.6 cmc)2.56 cmd)5.6 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.a)3.2 cmb)1.6 cmc)2.56 cmd)5.6 cmCorrect answer is option 'A'. Can you explain this answer?.
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