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A solid sphere of copper of radius 10.5 cm is melted and right cones of radius 3.5 cm and height 3 cm are made from the material. What is the number of cones made?
- a)136
- b)126
- c)156
- d)146
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A solid sphere of copper of radius 10.5 cm is melted and right cones o...
To find the number of cones made, we need to determine the volume of the solid sphere and the volume of each cone. Then, we can divide the volume of the sphere by the volume of each cone to find the number of cones.
Given:
Radius of the sphere, r = 10.5 cm
Radius of the cone, R = 3.5 cm
Height of the cone, h = 3 cm
1. Find the volume of the sphere:
The volume of a sphere is given by the formula V = (4/3)πr³.
Substituting the value of the radius, we get V = (4/3)π(10.5)³.
2. Find the volume of each cone:
The volume of a cone is given by the formula V = (1/3)πR²h.
Substituting the values of the radius and height, we get V = (1/3)π(3.5)²(3).
3. Find the number of cones:
To find the number of cones, we divide the volume of the sphere by the volume of each cone:
Number of cones = (Volume of the sphere) / (Volume of each cone).
Let's calculate the values:
1. Volume of the sphere:
V = (4/3)π(10.5)³ = (4/3)π(1157.625) = 1543.5π cm³
2. Volume of each cone:
V = (1/3)π(3.5)²(3) = (1/3)π(12.25)(3) = 12.25π cm³
3. Number of cones:
Number of cones = 1543.5π / 12.25π = 126
Therefore, the number of cones made from the material is 126 cones, which corresponds to option B.
Given:
Radius of the sphere, r = 10.5 cm
Radius of the cone, R = 3.5 cm
Height of the cone, h = 3 cm
1. Find the volume of the sphere:
The volume of a sphere is given by the formula V = (4/3)πr³.
Substituting the value of the radius, we get V = (4/3)π(10.5)³.
2. Find the volume of each cone:
The volume of a cone is given by the formula V = (1/3)πR²h.
Substituting the values of the radius and height, we get V = (1/3)π(3.5)²(3).
3. Find the number of cones:
To find the number of cones, we divide the volume of the sphere by the volume of each cone:
Number of cones = (Volume of the sphere) / (Volume of each cone).
Let's calculate the values:
1. Volume of the sphere:
V = (4/3)π(10.5)³ = (4/3)π(1157.625) = 1543.5π cm³
2. Volume of each cone:
V = (1/3)π(3.5)²(3) = (1/3)π(12.25)(3) = 12.25π cm³
3. Number of cones:
Number of cones = 1543.5π / 12.25π = 126
Therefore, the number of cones made from the material is 126 cones, which corresponds to option B.
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A solid sphere of copper of radius 10.5 cm is melted and right cones o...
Let the number of cones made be n. The volume of solid sphere = volume of resulting cones
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A solid sphere of copper of radius 10.5 cm is melted and right cones of radius 3.5 cm and height 3 cm are made from the material. What is the number of cones made?a)136b)126c)156d)146Correct answer is option 'B'. Can you explain this answer?
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