CAT Exam > CAT Questions > A solid sphere of radius 3 cm is melted to f...
Start Learning for Free
A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.
- a)3 cm
- b)4 cm
- c)5 cm
- d)6 cm
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A solid sphere of radius 3 cm is melted to form a right circular cone...
Given,
View all questions of this test
Radius of sphere = 3 cm
Height of the cone = Half of the radius of the cone
Volume of Sphere = Volume of Cone
Volume of Sphere
= 4/3 × πR3
Volume of Cone
=1/3 × πr2h
Suppose the height and radius of the cone are ' h ' and ' r ' respectively.
∴ h = r/2
Applying the formula:
43 × π × 3 × 3 × 3 = 1/3 × π × r × r × h
Put
h = r/2
⇒ 4/3 × 3 × 3 × 3 = 1 / 3 × r × r × r/2
⇒ r3 = 216
⇒ r = 6
∴ Radius of the cone =6 cm.
Hence, the correct option is (D).
Most Upvoted Answer
A solid sphere of radius 3 cm is melted to form a right circular cone...
To solve this problem, let's break it down into steps:
Step 1: Find the volume of the solid sphere.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, the radius of the sphere is 3 cm, so the volume of the sphere is V = (4/3)π(3^3) = (4/3)π(27) = 36π cm³.
Step 2: Find the height of the cone.
According to the given information, the height of the cone is half the radius of the cone. Since the radius of the sphere is 3 cm, the height of the cone is 3/2 = 1.5 cm.
Step 3: Find the volume of the cone.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. In this case, the height of the cone is 1.5 cm, and we need to find the radius of the cone.
Step 4: Substitute the known values into the volume formula of the cone.
We know that the volume of the cone is equal to the volume of the sphere, so we can set up the equation:
(1/3)πr^2(1.5) = 36π
Step 5: Simplify and solve for r.
Dividing both sides of the equation by (1/3)π(1.5), we get:
r^2 = 36/1.5
r^2 = 24
Taking the square root of both sides, we get:
r = √24
r ≈ 4.9 cm
Therefore, the radius of the cone is approximately 4.9 cm, which is closest to option (D) 6 cm.
Step 1: Find the volume of the solid sphere.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, the radius of the sphere is 3 cm, so the volume of the sphere is V = (4/3)π(3^3) = (4/3)π(27) = 36π cm³.
Step 2: Find the height of the cone.
According to the given information, the height of the cone is half the radius of the cone. Since the radius of the sphere is 3 cm, the height of the cone is 3/2 = 1.5 cm.
Step 3: Find the volume of the cone.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. In this case, the height of the cone is 1.5 cm, and we need to find the radius of the cone.
Step 4: Substitute the known values into the volume formula of the cone.
We know that the volume of the cone is equal to the volume of the sphere, so we can set up the equation:
(1/3)πr^2(1.5) = 36π
Step 5: Simplify and solve for r.
Dividing both sides of the equation by (1/3)π(1.5), we get:
r^2 = 36/1.5
r^2 = 24
Taking the square root of both sides, we get:
r = √24
r ≈ 4.9 cm
Therefore, the radius of the cone is approximately 4.9 cm, which is closest to option (D) 6 cm.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer?
Question Description
A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer?.
A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT 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