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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?
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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?
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