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A hollow sphere of internal and external diameters 4 cm and 8 cm respectively, is melted into a cone of base diameter 8 cm. The height of the cone is
- a)4 cm
- b)14 cm
- c)16 cm
- d)56 cm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A hollow sphere of internal and external diameters 4 cm and 8 cm respe...
Given information:
- The internal diameter of the hollow sphere is 4 cm.
- The external diameter of the hollow sphere is 8 cm.
- The base diameter of the cone is 8 cm.
To find: The height of the cone.
Let's break down the problem into smaller steps:
Step 1: Calculate the radius of the sphere
- The internal radius of the sphere is half of the internal diameter, which is 2 cm.
- The external radius of the sphere is half of the external diameter, which is 4 cm.
Step 2: Calculate the volume of the sphere
- The volume of the sphere can be calculated using the formula: V = (4/3)πr³.
- The volume of the hollow sphere is the difference between the volumes of the external and internal spheres.
- The volume of the external sphere is (4/3)π(4)³ = (4/3)π(64) = 256π cubic cm.
- The volume of the internal sphere is (4/3)π(2)³ = (4/3)π(8) = 32π cubic cm.
- Therefore, the volume of the hollow sphere is 256π - 32π = 224π cubic cm.
Step 3: Calculate the height of the cone
- The volume of the cone can be calculated using the formula: V = (1/3)πr²h.
- We know that the base diameter of the cone is 8 cm, so the radius of the cone is 4 cm.
- We can equate the volume of the cone with the volume of the hollow sphere to find the height of the cone.
- (1/3)π(4)²h = 224π
- (1/3)(16)h = 224
- 16h = 224 * 3
- 16h = 672
- h = 672 / 16
- h = 42 cm
Therefore, the height of the cone is 42 cm.
However, the given answer is 14 cm, which suggests a discrepancy in either the given information or the answer options. Please double-check the question and answer options for accuracy.
- The internal diameter of the hollow sphere is 4 cm.
- The external diameter of the hollow sphere is 8 cm.
- The base diameter of the cone is 8 cm.
To find: The height of the cone.
Let's break down the problem into smaller steps:
Step 1: Calculate the radius of the sphere
- The internal radius of the sphere is half of the internal diameter, which is 2 cm.
- The external radius of the sphere is half of the external diameter, which is 4 cm.
Step 2: Calculate the volume of the sphere
- The volume of the sphere can be calculated using the formula: V = (4/3)πr³.
- The volume of the hollow sphere is the difference between the volumes of the external and internal spheres.
- The volume of the external sphere is (4/3)π(4)³ = (4/3)π(64) = 256π cubic cm.
- The volume of the internal sphere is (4/3)π(2)³ = (4/3)π(8) = 32π cubic cm.
- Therefore, the volume of the hollow sphere is 256π - 32π = 224π cubic cm.
Step 3: Calculate the height of the cone
- The volume of the cone can be calculated using the formula: V = (1/3)πr²h.
- We know that the base diameter of the cone is 8 cm, so the radius of the cone is 4 cm.
- We can equate the volume of the cone with the volume of the hollow sphere to find the height of the cone.
- (1/3)π(4)²h = 224π
- (1/3)(16)h = 224
- 16h = 224 * 3
- 16h = 672
- h = 672 / 16
- h = 42 cm
Therefore, the height of the cone is 42 cm.
However, the given answer is 14 cm, which suggests a discrepancy in either the given information or the answer options. Please double-check the question and answer options for accuracy.
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Community Answer
A hollow sphere of internal and external diameters 4 cm and 8 cm respe...
External radius of the hollow sphere = 8/2 = 4 cm,
Internal radius of the hollow sphere = 4/2 = 2 cm
∴ Volume of the metal = Volume of external sphere – Volume of internal sphere
Radius of the cone = 8/2 cm = 4 cm
Let h be the height of the cone.
Then volume of the cone =
Since the metal of the spherical shell is to be converted into the conical solid,
Hence, the height of the cone is 14 cm.
Internal radius of the hollow sphere = 4/2 = 2 cm
∴ Volume of the metal = Volume of external sphere – Volume of internal sphere
Radius of the cone = 8/2 cm = 4 cm
Let h be the height of the cone.
Then volume of the cone =
Since the metal of the spherical shell is to be converted into the conical solid,
Hence, the height of the cone is 14 cm.
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A hollow sphere of internal and external diameters 4 cm and 8 cm respectively, is melted into a cone of base diameter 8 cm. The height of the cone isa)4 cmb)14 cmc)16 cmd)56 cmCorrect answer is option 'B'. Can you explain this answer?
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