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A solid metal cone with base-radius 12 cm and height 24 cm, is melted to form solid spherical balls, each of diameters 6 cm. The number of such balls made is
- a)32
- b)36
- c)48
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A solid metal cone with base-radius 12 cm and height 24 cm, is melted ...
Concept: The volume of a cone is given by the formula V = 1/3πr²h, where r is the radius of the base and h is the height. The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere.
Given: The base-radius of the cone is 12 cm and the height is 24 cm. The diameter of each spherical ball is 6 cm.
To find: The number of spherical balls that can be made from the cone.
Solution:
Step 1: Find the volume of the cone using the formula V = 1/3πr²h.
V = 1/3 x π x 12² x 24
= 1/3 x π x 144 x 24
= 1/3 x π x 3456
= 1152π
Therefore, the volume of the cone is 1152π cubic cm.
Step 2: Find the volume of each spherical ball using the formula V = 4/3πr³.
The diameter of each spherical ball is 6 cm, so the radius is 3 cm.
V = 4/3 x π x 3³
= 4/3 x π x 27
= 36π
Therefore, the volume of each spherical ball is 36π cubic cm.
Step 3: Find the number of spherical balls that can be made from the cone.
Number of balls = (Volume of cone) / (Volume of each ball)
= (1152π) / (36π)
= 32
Answer: The number of spherical balls that can be made from the cone is 32. Therefore, the correct option is (a).
Given: The base-radius of the cone is 12 cm and the height is 24 cm. The diameter of each spherical ball is 6 cm.
To find: The number of spherical balls that can be made from the cone.
Solution:
Step 1: Find the volume of the cone using the formula V = 1/3πr²h.
V = 1/3 x π x 12² x 24
= 1/3 x π x 144 x 24
= 1/3 x π x 3456
= 1152π
Therefore, the volume of the cone is 1152π cubic cm.
Step 2: Find the volume of each spherical ball using the formula V = 4/3πr³.
The diameter of each spherical ball is 6 cm, so the radius is 3 cm.
V = 4/3 x π x 3³
= 4/3 x π x 27
= 36π
Therefore, the volume of each spherical ball is 36π cubic cm.
Step 3: Find the number of spherical balls that can be made from the cone.
Number of balls = (Volume of cone) / (Volume of each ball)
= (1152π) / (36π)
= 32
Answer: The number of spherical balls that can be made from the cone is 32. Therefore, the correct option is (a).
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Community Answer
A solid metal cone with base-radius 12 cm and height 24 cm, is melted ...
Problem: A solid metal cone with base-radius 12 cm and height 24 cm, is melted to form solid spherical balls, each of diameters 6 cm. The number of such balls made is
Solution:
Let's calculate the volume of the cone first:
Volume of cone = (1/3)πr²h
= (1/3) x 22/7 x 12² x 24
= 110592/7
We know that the volume of each spherical ball is (4/3)πr³, where r = 3 cm (diameter = 6 cm)
So, the volume of each spherical ball = (4/3) x 22/7 x 3³
= 113.14
To find the number of spherical balls that can be made, we need to divide the volume of the cone by the volume of each spherical ball:
Number of spherical balls = Volume of cone / Volume of each spherical ball
= (110592/7) / 113.14
= 32
Therefore, the number of such balls made is 32. Hence, the correct option is (a).
Solution:
Let's calculate the volume of the cone first:
Volume of cone = (1/3)πr²h
= (1/3) x 22/7 x 12² x 24
= 110592/7
We know that the volume of each spherical ball is (4/3)πr³, where r = 3 cm (diameter = 6 cm)
So, the volume of each spherical ball = (4/3) x 22/7 x 3³
= 113.14
To find the number of spherical balls that can be made, we need to divide the volume of the cone by the volume of each spherical ball:
Number of spherical balls = Volume of cone / Volume of each spherical ball
= (110592/7) / 113.14
= 32
Therefore, the number of such balls made is 32. Hence, the correct option is (a).
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A solid metal cone with base-radius 12 cm and height 24 cm, is melted to form solid spherical balls, each of diameters 6 cm. The number of such balls made isa)32b)36c)48d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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