Class 10 Exam > Class 10 Questions > A solid metal cone with base-radius 12 cm and...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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).
Free Test
FREE
| Start Free Test |
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).
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
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?
Question Description
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? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 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? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 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? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup