Class 10 Exam > Class 10 Questions > A cylinder, a cone and a hemisphere have equa...
Start Learning for Free
A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumes
- a)1:1:1
- b)2:3:1
- c)3 :1 :2
- d)1:2:3
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A cylinder, a cone and a hemisphere have equal base and height. Find t...
**Given**
- A cylinder, a cone, and a hemisphere have equal base and height.
**To Find**
- The ratio of their volumes.
**Solution**
Let's assume the height and base radius of each shape to be 'h' and 'r', respectively.
**Volume of a Cylinder**
The volume of a cylinder is given by the formula:
Vcylinder = πr^2h
**Volume of a Cone**
The volume of a cone is given by the formula:
Vcone = (1/3)πr^2h
**Volume of a Hemisphere**
The volume of a hemisphere is given by the formula:
Vhemisphere = (2/3)πr^3
**Given Conditions**
- The base radius and height of the cylinder, cone, and hemisphere are equal.
- So, r = h for all three shapes.
**Substituting Values**
Substituting r = h in the volume formulas for each shape, we get:
Vcylinder = πr^2h = πh^2h = πh^3
Vcone = (1/3)πr^2h = (1/3)πh^2h = (1/3)πh^3
Vhemisphere = (2/3)πr^3 = (2/3)πh^3
**Comparing Volumes**
The ratio of the volumes of the cylinder, cone, and hemisphere can be found by dividing each volume by the volume of the cylinder (since the cylinder has the largest volume):
Ratio = (Vcylinder : Vcone : Vhemisphere) / Vcylinder
= (πh^3 : (1/3)πh^3 : (2/3)πh^3) / πh^3
= 1 : (1/3) : (2/3)
= 3 : 1 : 2
Therefore, the ratio of their volumes is 3 : 1 : 2. The correct answer is option 'C'.
- A cylinder, a cone, and a hemisphere have equal base and height.
**To Find**
- The ratio of their volumes.
**Solution**
Let's assume the height and base radius of each shape to be 'h' and 'r', respectively.
**Volume of a Cylinder**
The volume of a cylinder is given by the formula:
Vcylinder = πr^2h
**Volume of a Cone**
The volume of a cone is given by the formula:
Vcone = (1/3)πr^2h
**Volume of a Hemisphere**
The volume of a hemisphere is given by the formula:
Vhemisphere = (2/3)πr^3
**Given Conditions**
- The base radius and height of the cylinder, cone, and hemisphere are equal.
- So, r = h for all three shapes.
**Substituting Values**
Substituting r = h in the volume formulas for each shape, we get:
Vcylinder = πr^2h = πh^2h = πh^3
Vcone = (1/3)πr^2h = (1/3)πh^2h = (1/3)πh^3
Vhemisphere = (2/3)πr^3 = (2/3)πh^3
**Comparing Volumes**
The ratio of the volumes of the cylinder, cone, and hemisphere can be found by dividing each volume by the volume of the cylinder (since the cylinder has the largest volume):
Ratio = (Vcylinder : Vcone : Vhemisphere) / Vcylinder
= (πh^3 : (1/3)πh^3 : (2/3)πh^3) / πh^3
= 1 : (1/3) : (2/3)
= 3 : 1 : 2
Therefore, the ratio of their volumes is 3 : 1 : 2. The correct answer is option 'C'.
Free Test
FREE
| Start Free Test |
Community Answer
A cylinder, a cone and a hemisphere have equal base and height. Find t...
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 cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. Can you explain this answer?
Question Description
A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. 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 cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. 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 cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. Can you explain this answer?.
A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. 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 cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. 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 cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. Can you explain this answer?.
Solutions for A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. 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 cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumesa)1:1:1b)2:3:1c)3 :1 :2d)1:2:3Correct answer is option 'C'. 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!
within 7 days!
Takes less than 10 seconds to signup