Class 10 Exam > Class 10 Questions > The volume of a right cylinder with its heigh...
Start Learning for Free
The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.?
Most Upvoted Answer
The volume of a right cylinder with its height equal to the radius is ...
Understanding the Problem
To find the height of a right cylinder where the height is equal to the radius and the volume is given as 25 1/7 cm³, we need to use the formula for the volume of a cylinder.
Volume Formula
The formula for the volume (V) of a cylinder is:
V = πr²h
Where:
- V = volume
- r = radius
- h = height
Since the height is equal to the radius (h = r), we can substitute h with r in the formula.
Substituting Values
Given that h = r, we can rewrite the volume formula as:
V = πr²r
V = πr³
Now substituting the given volume and the value of π:
V = 25 1/7 cm³ = 25.14 cm³ (approximately)
π = 22/7
So the equation becomes:
25.14 = (22/7)r³
Solving for r
To isolate r, we can rearrange the equation:
r³ = (25.14 * 7) / 22
r³ = 176.98 / 22
r³ ≈ 8.045
Now, we find the cube root of r³:
r ≈ 2 cm (approximately)
Finding the Height
Since the height (h) is equal to the radius (r):
h = r ≈ 2 cm
Conclusion
The height of the cylinder is approximately 2 cm.
To find the height of a right cylinder where the height is equal to the radius and the volume is given as 25 1/7 cm³, we need to use the formula for the volume of a cylinder.
Volume Formula
The formula for the volume (V) of a cylinder is:
V = πr²h
Where:
- V = volume
- r = radius
- h = height
Since the height is equal to the radius (h = r), we can substitute h with r in the formula.
Substituting Values
Given that h = r, we can rewrite the volume formula as:
V = πr²r
V = πr³
Now substituting the given volume and the value of π:
V = 25 1/7 cm³ = 25.14 cm³ (approximately)
π = 22/7
So the equation becomes:
25.14 = (22/7)r³
Solving for r
To isolate r, we can rearrange the equation:
r³ = (25.14 * 7) / 22
r³ = 176.98 / 22
r³ ≈ 8.045
Now, we find the cube root of r³:
r ≈ 2 cm (approximately)
Finding the Height
Since the height (h) is equal to the radius (r):
h = r ≈ 2 cm
Conclusion
The height of the cylinder is approximately 2 cm.
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
The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.?
Question Description
The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? 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 The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.?.
The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? 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 The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.?.
Solutions for The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? 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 The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? defined & explained in the simplest way possible. Besides giving the explanation of
The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.?, a detailed solution for The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? has been provided alongside types of The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? theory, EduRev gives you an
ample number of questions to practice The volume of a right cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Take pie = 22/7.) class 10.? 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup