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A solid metallic cylinder of base radius 3cm and height 5cm is melted to make a solid cone of height 1cm and base radius 1mm. What is the number of cones?
- a)1350
- b)4500
- c)13500
- d)450
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A solid metallic cylinder of base radius 3cm and height 5cm is melted ...
Number of cones
= 3 × 3 × 3 × 5 × 10 × 10
= 135 × 100
= 13500
= 3 × 3 × 3 × 5 × 10 × 10
= 135 × 100
= 13500
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Community Answer
A solid metallic cylinder of base radius 3cm and height 5cm is melted ...
Volume of the Cylinder
To find the number of cones that can be made from the cylinder, we first calculate the volume of the cylinder.
- Formula for the volume of a cylinder:
Volume = πr²h
- Given:
Base radius (r) = 3 cm
Height (h) = 5 cm
- Calculation:
Volume of cylinder = π * (3)² * 5
= π * 9 * 5
= 45π cm³
Volume of the Cone
Next, we calculate the volume of one cone made from the melted cylinder.
- Formula for the volume of a cone:
Volume = (1/3)πr²h
- Given:
Base radius (r) = 1 mm = 0.1 cm (conversion from mm to cm)
Height (h) = 1 cm
- Calculation:
Volume of cone = (1/3) * π * (0.1)² * 1
= (1/3) * π * 0.01
= (0.01/3)π cm³
Finding the Number of Cones
Now, we find out how many such cones can be formed from the volume of the cylinder.
- Total number of cones = Volume of Cylinder / Volume of one Cone
= (45π) / ((0.01/3)π)
= 45 / (0.01/3)
= 45 * (3/0.01)
= 45 * 300
= 13500
Conclusion
Thus, the total number of cones that can be made is 13500, which corresponds to option 'C'.
To find the number of cones that can be made from the cylinder, we first calculate the volume of the cylinder.
- Formula for the volume of a cylinder:
Volume = πr²h
- Given:
Base radius (r) = 3 cm
Height (h) = 5 cm
- Calculation:
Volume of cylinder = π * (3)² * 5
= π * 9 * 5
= 45π cm³
Volume of the Cone
Next, we calculate the volume of one cone made from the melted cylinder.
- Formula for the volume of a cone:
Volume = (1/3)πr²h
- Given:
Base radius (r) = 1 mm = 0.1 cm (conversion from mm to cm)
Height (h) = 1 cm
- Calculation:
Volume of cone = (1/3) * π * (0.1)² * 1
= (1/3) * π * 0.01
= (0.01/3)π cm³
Finding the Number of Cones
Now, we find out how many such cones can be formed from the volume of the cylinder.
- Total number of cones = Volume of Cylinder / Volume of one Cone
= (45π) / ((0.01/3)π)
= 45 / (0.01/3)
= 45 * (3/0.01)
= 45 * 300
= 13500
Conclusion
Thus, the total number of cones that can be made is 13500, which corresponds to option 'C'.
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A solid metallic cylinder of base radius 3cm and height 5cm is melted to make a solid cone of height 1cm and base radius 1mm. What is the number of cones?a)1350b)4500c)13500d)450Correct answer is option 'C'. Can you explain this answer?
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