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A solid metallic cylinder of base radius 5 cm and height 7 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones?
- a)53500
- b)49500
- c)51500
- d)52500
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A solid metallic cylinder of base radius 5 cm and height 7 cm is melte...
Number of cones =Volume of Cylinder / Volume of one cone
= π*5*5*7 / (1/3π * 1/10 * 1/10 * 1)
= 52500
= π*5*5*7 / (1/3π * 1/10 * 1/10 * 1)
= 52500
Most Upvoted Answer
A solid metallic cylinder of base radius 5 cm and height 7 cm is melte...
To solve this problem, we need to find the number of cones that can be formed by melting a solid metallic cylinder.
Given:
Base radius of the cylinder = 5 cm
Height of the cylinder = 7 cm
Height of each cone = 1 cm
Base radius of each cone = 1 mm = 0.1 cm
We can start by finding the volume of the cylinder and the volume of each cone.
1. Volume of the cylinder:
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the base radius and h is the height. In this case, the radius of the cylinder is 5 cm and the height is 7 cm.
So the volume of the cylinder is V_cylinder = π(5^2)(7) = 175π cm^3.
2. Volume of each cone:
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the base radius and h is the height. In this case, the radius of each cone is 0.1 cm and the height is 1 cm.
So the volume of each cone is V_cone = (1/3)π(0.1^2)(1) = (1/300)π cm^3.
Next, we need to find the number of cones that can be formed by dividing the volume of the cylinder by the volume of each cone.
3. Number of cones:
Number of cones = V_cylinder / V_cone
Number of cones = (175π) / ((1/300)π) = 52500
Therefore, the number of cones that can be formed is 52500.
Hence, the correct answer is option D) 52500.
Given:
Base radius of the cylinder = 5 cm
Height of the cylinder = 7 cm
Height of each cone = 1 cm
Base radius of each cone = 1 mm = 0.1 cm
We can start by finding the volume of the cylinder and the volume of each cone.
1. Volume of the cylinder:
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the base radius and h is the height. In this case, the radius of the cylinder is 5 cm and the height is 7 cm.
So the volume of the cylinder is V_cylinder = π(5^2)(7) = 175π cm^3.
2. Volume of each cone:
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the base radius and h is the height. In this case, the radius of each cone is 0.1 cm and the height is 1 cm.
So the volume of each cone is V_cone = (1/3)π(0.1^2)(1) = (1/300)π cm^3.
Next, we need to find the number of cones that can be formed by dividing the volume of the cylinder by the volume of each cone.
3. Number of cones:
Number of cones = V_cylinder / V_cone
Number of cones = (175π) / ((1/300)π) = 52500
Therefore, the number of cones that can be formed is 52500.
Hence, the correct answer is option D) 52500.
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A solid metallic cylinder of base radius 5 cm and height 7 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones?a)53500b)49500c)51500d)52500e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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