Railways Exam > Railways Questions > Three toys are in the shape of the cylinder,...
Start Learning for Free
Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?
- a)4 : 3 : √2 +1
- b)4 : 3 : 2 + √2
- c)4 : 3 : 2 √2
- d)2 : 1 : √2 + 1
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Three toys are in the shape of the cylinder, hemisphere, and cone . T...
Height of each toy = 2√2
since height of hemisphere = radius of hemisphere
= radius of each toy = 2√2
slant height of cone(l)
ratio = T.S.A of cylinder: T.S.A of the hemisphere : T.S.A of cone
Most Upvoted Answer
Three toys are in the shape of the cylinder, hemisphere, and cone . T...
The Ratio of Total Surface Areas of the Cylinder, Hemisphere, and Cone
To find the ratio of the total surface areas of the cylinder, hemisphere, and cone, we need to calculate the individual surface areas of each shape and then compare them.
Given:
- The three toys have the same base.
- The height of each toy is 2√2.
Surface Area of a Cylinder:
The surface area of a cylinder is given by the formula:
A = 2πrh + πr^2, where r is the radius and h is the height.
Since the three toys have the same base, their radii will also be the same. Let's assume the radius of each toy is 'r'.
The height of each toy is given as 2√2, so the surface area of the cylinder will be:
A_cylinder = 2πr(2√2) + πr^2
= 4πr√2 + πr^2
Surface Area of a Hemisphere:
The surface area of a hemisphere is given by the formula:
A = 2πr^2, where r is the radius.
Since the three toys have the same base, their radii will also be the same. Let's assume the radius of each toy is 'r'.
The surface area of the hemisphere will be:
A_hemisphere = 2πr^2
Surface Area of a Cone:
The surface area of a cone is given by the formula:
A = πrl + πr^2, where r is the radius and l is the slant height.
Since the three toys have the same base, their radii will also be the same. Let's assume the radius of each toy is 'r'.
The height of each toy is given as 2√2, so the slant height of the cone will be:
l = √(r^2 + (2√2)^2)
= √(r^2 + 8)
The surface area of the cone will be:
A_cone = πr(√(r^2 + 8)) + πr^2
= πr√(r^2 + 8) + πr^2
Calculating the Ratio:
To calculate the ratio of the total surface areas, we need to add up the surface areas of the cylinder, hemisphere, and cone and then compare them.
Total surface area = A_cylinder + A_hemisphere + A_cone
Plugging in the formulas we derived earlier, we get:
Total surface area = (4πr√2 + πr^2) + (2πr^2) + (πr√(r^2 + 8) + πr^2)
Now, simplify the expression and factor out common terms:
Total surface area = 4πr√2 + 2πr^2 + πr√(r^2 + 8)
Now, we can calculate the ratio of the total surface areas by dividing each term by the total surface area:
Ratio = (4πr√2) / (4πr√2 + 2πr^2 + πr√(r^2 + 8))
To find the ratio of the total surface areas of the cylinder, hemisphere, and cone, we need to calculate the individual surface areas of each shape and then compare them.
Given:
- The three toys have the same base.
- The height of each toy is 2√2.
Surface Area of a Cylinder:
The surface area of a cylinder is given by the formula:
A = 2πrh + πr^2, where r is the radius and h is the height.
Since the three toys have the same base, their radii will also be the same. Let's assume the radius of each toy is 'r'.
The height of each toy is given as 2√2, so the surface area of the cylinder will be:
A_cylinder = 2πr(2√2) + πr^2
= 4πr√2 + πr^2
Surface Area of a Hemisphere:
The surface area of a hemisphere is given by the formula:
A = 2πr^2, where r is the radius.
Since the three toys have the same base, their radii will also be the same. Let's assume the radius of each toy is 'r'.
The surface area of the hemisphere will be:
A_hemisphere = 2πr^2
Surface Area of a Cone:
The surface area of a cone is given by the formula:
A = πrl + πr^2, where r is the radius and l is the slant height.
Since the three toys have the same base, their radii will also be the same. Let's assume the radius of each toy is 'r'.
The height of each toy is given as 2√2, so the slant height of the cone will be:
l = √(r^2 + (2√2)^2)
= √(r^2 + 8)
The surface area of the cone will be:
A_cone = πr(√(r^2 + 8)) + πr^2
= πr√(r^2 + 8) + πr^2
Calculating the Ratio:
To calculate the ratio of the total surface areas, we need to add up the surface areas of the cylinder, hemisphere, and cone and then compare them.
Total surface area = A_cylinder + A_hemisphere + A_cone
Plugging in the formulas we derived earlier, we get:
Total surface area = (4πr√2 + πr^2) + (2πr^2) + (πr√(r^2 + 8) + πr^2)
Now, simplify the expression and factor out common terms:
Total surface area = 4πr√2 + 2πr^2 + πr√(r^2 + 8)
Now, we can calculate the ratio of the total surface areas by dividing each term by the total surface area:
Ratio = (4πr√2) / (4πr√2 + 2πr^2 + πr√(r^2 + 8))
Attention Railways Students!
To make sure you are not studying endlessly, EduRev has designed Railways study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Railways.
|
Explore Courses for Railways exam
|
|
Similar Railways Doubts
Top Courses for RailwaysView all
Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer?
Question Description
Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer?.
Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer?.
Solutions for Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
Download more important topics, notes, lectures and mock test series for Railways Exam by signing up for free.
Here you can find the meaning of Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Three toys are in the shape of the cylinder, hemisphere, and cone . The three toys have the same base. The height of each toy is 2 √2. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively ?a)4 : 3 : √2 +1b)4 : 3 : 2 + √2c)4 : 3 : 2 √2d)2 : 1 : √2 + 1Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Railways tests.
|
|
Explore Courses for Railways 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