UCAT Exam > UCAT Questions > If the base of a cylinder is the same as that...
Start Learning for Free
If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.
- a)1 : 3
- b)3 : 2
- c)3 : 1
- d)2 : 3
- e)Not Attempted
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the base of a cylinder is the same as that of a cone, and the heigh...
Here, let radius of cylinder and radius of cone be r1 and r2 respectively
Also, height of the cylinder and cone be h1 and h2 respectively
As, base of a cylinder = base of a cone
⇒ π r12 = π r22 ⇔ r12 = r22
⇒ r1 = r2
Also, it is given height is same. So, h1 = h2.
⇒ Volume of the cylinder = π r12 h1
⇒ Volume of the cone = 1/3 π r22 h2
⇒ Ratio of volume of the cylinder and volume of the cone = π r12 h1 : 1/3 π r12 h1 = 1 :1/3 = 3 :1.
Hence, the ratio of volume of the cylinder and volume of the cone = 3 :1.
Most Upvoted Answer
If the base of a cylinder is the same as that of a cone, and the heigh...
Here, let radius of cylinder and radius of cone be r1 and r2 respectively
Also, height of the cylinder and cone be h1 and h2 respectively
As, base of a cylinder = base of a cone
⇒ π r12 = π r22 ⇔ r12 = r22
⇒ r1 = r2
Also, it is given height is same. So, h1 = h2.
⇒ Volume of the cylinder = π r12 h1
⇒ Volume of the cone = 1/3 π r22 h2
⇒ Ratio of volume of the cylinder and volume of the cone = π r12 h1 : 1/3 π r12 h1 = 1 :1/3 = 3 :1.
Hence, the ratio of volume of the cylinder and volume of the cone = 3 :1.
Free Test
FREE
| Start Free Test |
Community Answer
If the base of a cylinder is the same as that of a cone, and the heigh...
Understanding the Volumes of Cylinder and Cone
To find the ratio of the volumes of a cylinder and a cone with the same base radius and height, we need to use the formulas for their volumes.
Volume Formulas
- Volume of a Cylinder:
The formula is V_cylinder = πr²h, where r is the radius and h is the height.
- Volume of a Cone:
The formula is V_cone = (1/3)πr²h.
Given Conditions
- Both the cylinder and the cone have the same base radius (r) and the same height (h).
Calculating Volumes
1. Volume of the Cylinder:
- V_cylinder = πr²h.
2. Volume of the Cone:
- V_cone = (1/3)πr²h.
Finding the Ratio
Now, we can express the ratio of the volumes of the cylinder to the cone:
- Ratio = V_cylinder / V_cone
- = (πr²h) / ((1/3)πr²h)
- = (πr²h) * (3/(πr²h))
- = 3.
Thus, the ratio of the volume of the cylinder to the volume of the cone is 3:1.
Conclusion
The correct answer is option 'C', which indicates that the volume of the cylinder is three times that of the cone, expressed as a ratio of 3:1.
To find the ratio of the volumes of a cylinder and a cone with the same base radius and height, we need to use the formulas for their volumes.
Volume Formulas
- Volume of a Cylinder:
The formula is V_cylinder = πr²h, where r is the radius and h is the height.
- Volume of a Cone:
The formula is V_cone = (1/3)πr²h.
Given Conditions
- Both the cylinder and the cone have the same base radius (r) and the same height (h).
Calculating Volumes
1. Volume of the Cylinder:
- V_cylinder = πr²h.
2. Volume of the Cone:
- V_cone = (1/3)πr²h.
Finding the Ratio
Now, we can express the ratio of the volumes of the cylinder to the cone:
- Ratio = V_cylinder / V_cone
- = (πr²h) / ((1/3)πr²h)
- = (πr²h) * (3/(πr²h))
- = 3.
Thus, the ratio of the volume of the cylinder to the volume of the cone is 3:1.
Conclusion
The correct answer is option 'C', which indicates that the volume of the cylinder is three times that of the cone, expressed as a ratio of 3:1.
|
Explore Courses for UCAT exam
|
|
Top Courses for UCATView all
Question Description
If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer?.
If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer?.
Solutions for If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UCAT.
Download more important topics, notes, lectures and mock test series for UCAT Exam by signing up for free.
Here you can find the meaning of If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.a)1 : 3b)3 : 2c)3 : 1d)2 : 3e)Not AttemptedCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice UCAT tests.
|
|
Explore Courses for UCAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup