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A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?
Correct answer is '180'. Can you explain this answer?
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Verified Answer
A solid hemisphere of radius 0.3 metres is molten and recast into smal...
Let's convert everything to cm.
Volume of the hemisphere
Volume of each hollow cylinder = π R2h − π r2h = π (R2 − r2)h = π (49 − 9)2.5 = 100π
Hence, number of hollow cylinders that can be formed
Volume of the hemisphere
Volume of each hollow cylinder = π R2h − π r2h = π (R2 − r2)h = π (49 − 9)2.5 = 100π
Hence, number of hollow cylinders that can be formed
Most Upvoted Answer
A solid hemisphere of radius 0.3 metres is molten and recast into smal...
Given:
- Radius of solid hemisphere = 0.3 meters
- Outer diameter of hollow cylinders = 14 cm
- Inner diameter of hollow cylinders = 6 cm
- Height of hollow cylinders = 2.5 cm
To find:
- Maximum number of hollow cylinders that can be formed
Solution:
To find the maximum number of hollow cylinders that can be formed, we need to calculate the volume of the solid hemisphere and the volume of each hollow cylinder, and then divide the volume of the solid hemisphere by the volume of each hollow cylinder.
Volume of Solid Hemisphere:
The volume of a solid hemisphere is given by the formula:
V = (2/3) * π * r^3
Given that the radius of the solid hemisphere is 0.3 meters, we can substitute this value into the formula to find the volume:
V = (2/3) * π * (0.3)^3
V ≈ 0.0565 cubic meters
Volume of Hollow Cylinder:
The volume of a hollow cylinder can be calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder. The formula for the volume of a cylinder is:
V = π * r^2 * h
Volume of outer cylinder:
Radius = outer diameter / 2 = 14 / 2 = 7 cm = 0.07 meters
Height = 2.5 cm = 0.025 meters
V_outer = π * (0.07)^2 * 0.025
V_outer ≈ 0.0003848 cubic meters
Volume of inner cylinder:
Radius = inner diameter / 2 = 6 / 2 = 3 cm = 0.03 meters
Height = 2.5 cm = 0.025 meters
V_inner = π * (0.03)^2 * 0.025
V_inner ≈ 0.0000212 cubic meters
Volume of hollow cylinder = V_outer - V_inner
V_hollow = 0.0003848 - 0.0000212
V_hollow ≈ 0.0003636 cubic meters
Maximum Number of Hollow Cylinders:
Now, we can find the maximum number of hollow cylinders that can be formed by dividing the volume of the solid hemisphere by the volume of each hollow cylinder:
Number of hollow cylinders = V_solid / V_hollow
Number of hollow cylinders ≈ 0.0565 / 0.0003636
Number of hollow cylinders ≈ 155.5
However, since we are looking for the maximum number of hollow cylinders that can be formed, we need to round down to the nearest whole number. Therefore, the maximum number of hollow cylinders that can be formed is 155.
Thus, the correct answer is '155'.
- Radius of solid hemisphere = 0.3 meters
- Outer diameter of hollow cylinders = 14 cm
- Inner diameter of hollow cylinders = 6 cm
- Height of hollow cylinders = 2.5 cm
To find:
- Maximum number of hollow cylinders that can be formed
Solution:
To find the maximum number of hollow cylinders that can be formed, we need to calculate the volume of the solid hemisphere and the volume of each hollow cylinder, and then divide the volume of the solid hemisphere by the volume of each hollow cylinder.
Volume of Solid Hemisphere:
The volume of a solid hemisphere is given by the formula:
V = (2/3) * π * r^3
Given that the radius of the solid hemisphere is 0.3 meters, we can substitute this value into the formula to find the volume:
V = (2/3) * π * (0.3)^3
V ≈ 0.0565 cubic meters
Volume of Hollow Cylinder:
The volume of a hollow cylinder can be calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder. The formula for the volume of a cylinder is:
V = π * r^2 * h
Volume of outer cylinder:
Radius = outer diameter / 2 = 14 / 2 = 7 cm = 0.07 meters
Height = 2.5 cm = 0.025 meters
V_outer = π * (0.07)^2 * 0.025
V_outer ≈ 0.0003848 cubic meters
Volume of inner cylinder:
Radius = inner diameter / 2 = 6 / 2 = 3 cm = 0.03 meters
Height = 2.5 cm = 0.025 meters
V_inner = π * (0.03)^2 * 0.025
V_inner ≈ 0.0000212 cubic meters
Volume of hollow cylinder = V_outer - V_inner
V_hollow = 0.0003848 - 0.0000212
V_hollow ≈ 0.0003636 cubic meters
Maximum Number of Hollow Cylinders:
Now, we can find the maximum number of hollow cylinders that can be formed by dividing the volume of the solid hemisphere by the volume of each hollow cylinder:
Number of hollow cylinders = V_solid / V_hollow
Number of hollow cylinders ≈ 0.0565 / 0.0003636
Number of hollow cylinders ≈ 155.5
However, since we are looking for the maximum number of hollow cylinders that can be formed, we need to round down to the nearest whole number. Therefore, the maximum number of hollow cylinders that can be formed is 155.
Thus, the correct answer is '155'.
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A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?Correct answer is '180'. Can you explain this answer?
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A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?Correct answer is '180'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?Correct answer is '180'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?Correct answer is '180'. Can you explain this answer?.
A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?Correct answer is '180'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?Correct answer is '180'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?Correct answer is '180'. Can you explain this answer?.
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