CAT Exam > CAT Questions > A solid cylinder is melted & then 1000 id...
Start Learning for Free
A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?
- a)100 : 1
- b)10 : 1
- c)1000 : 1
- d)1 : 1
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A solid cylinder is melted & then 1000 identical small solid cylin...
Let R and H be the radius & height of the bigger cylinder respectively.
Let rand h be the radius & height of the smaller cylinder respectively.
Since the big solid cylinder is divided into 1000 identical small cylinders, the volume remains constant.
Let rand h be the radius & height of the smaller cylinder respectively.
Since the big solid cylinder is divided into 1000 identical small cylinders, the volume remains constant.
1000 x πr2h = πR2H
Therefore,
(R / r)2 = (H / h) = 1000.
But R / r = H / h
Therefore,
(R / r)3 = (H / h)3 = 1000
(R / r) = (H / h) = 10
Now the ratio of surface areas will be equal to the ratio of squares of their radii as (R/r) = {H/h) Ratio of surface areas = (R/r)2 = 102 = 100 : 1
(R / r)2 = (H / h) = 1000.
But R / r = H / h
Therefore,
(R / r)3 = (H / h)3 = 1000
(R / r) = (H / h) = 10
Now the ratio of surface areas will be equal to the ratio of squares of their radii as (R/r) = {H/h) Ratio of surface areas = (R/r)2 = 102 = 100 : 1
Hence, option 1.
Most Upvoted Answer
A solid cylinder is melted & then 1000 identical small solid cylin...
To form a solid cone. The height of the cylinder is h and the radius of the cylinder is r. The height of the cone is also h, but the radius of the cone is R. We want to find the relationship between r and R.
To solve this problem, we need to use the volume formula for each shape. The volume of a cylinder is given by Vcylinder = πr^2h, and the volume of a cone is given by Vcone = (1/3)πR^2h.
Since the cylinder is melted to form the cone, the volume of the cylinder should be equal to the volume of the cone. Therefore, we can set up the equation:
πr^2h = (1/3)πR^2h
We can cancel out the π and the h from both sides of the equation:
r^2 = (1/3)R^2
To find the relationship between r and R, we can take the square root of both sides of the equation:
√(r^2) = √((1/3)R^2)
Simplifying the equation:
|r| = (1/√3)|R|
Since we are dealing with physical dimensions, the radius cannot be negative. Therefore, we can ignore the absolute value signs:
r = (1/√3)R
So, the relationship between r and R is given by:
r = (1/√3)R
To solve this problem, we need to use the volume formula for each shape. The volume of a cylinder is given by Vcylinder = πr^2h, and the volume of a cone is given by Vcone = (1/3)πR^2h.
Since the cylinder is melted to form the cone, the volume of the cylinder should be equal to the volume of the cone. Therefore, we can set up the equation:
πr^2h = (1/3)πR^2h
We can cancel out the π and the h from both sides of the equation:
r^2 = (1/3)R^2
To find the relationship between r and R, we can take the square root of both sides of the equation:
√(r^2) = √((1/3)R^2)
Simplifying the equation:
|r| = (1/√3)|R|
Since we are dealing with physical dimensions, the radius cannot be negative. Therefore, we can ignore the absolute value signs:
r = (1/√3)R
So, the relationship between r and R is given by:
r = (1/√3)R
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
|
|
Similar CAT Doubts
Top Courses for CATView all
A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. Can you explain this answer?
Question Description
A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. 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 cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. 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 cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. Can you explain this answer?.
A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. 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 cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. 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 cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. Can you explain this answer?.
Solutions for A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. 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 cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A solid cylinder is melted & then 1000 identical small solid cylinders are made out of it. If the proportion in which the radius changes is same as in which the height changes, then what is the ratio of the surface areas of the bigger cylinder & to the surface area of one of the smaller cylinders?a)100 : 1b)10 : 1c)1000 : 1d)1 : 1Correct answer is option 'A'. 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