CAT Exam > CAT Questions > What is the area of a plane figure bounded b...
Start Learning for Free
What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?
- a)1 - (π/2) sq. units
- b)(π/3) - 1 sq. units
- c)1 - (π/4) sq. units
- d)π - 1 sq. units
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
What is the area of a plane figure bounded by circle centered at orig...
To find the area of the plane figure bounded by the circle and the line, we first need to find the points of intersection between the circle and the line.
The line Max(x, y) = 1 can be rewritten as two separate lines: x = 1 and y = 1.
To find the points of intersection, we substitute these equations into the equation of the circle:
x^2 + y^2 = 1
For x = 1, we have:
1^2 + y^2 = 1
y^2 = 0
y = 0
So, one point of intersection is (1, 0).
For y = 1, we have:
x^2 + 1^2 = 1
x^2 + 1 = 1
x^2 = 0
x = 0
So, another point of intersection is (0, 1).
Now, we have the two points of intersection: (1, 0) and (0, 1). These two points divide the circle into two segments.
To find the area of the bounded figure, we calculate the area of each segment and sum them.
The first segment is a triangle with base 1 and height 1 (formed by the points (1, 0), (0, 0), and (0, 1)). The area of a triangle is given by:
Area = (base * height) / 2
Area = (1 * 1) / 2
Area = 1/2
The second segment is a sector of the circle with radius 1 and central angle 90 degrees (formed by the points (0, 0), (1, 0), and (0, 1)). The area of a sector is given by:
Area = (radius^2 * angle) / 2
Area = (1^2 * 90) / 2
Area = 45
So, the total area of the bounded figure is:
Total Area = Area of Triangle + Area of Sector
Total Area = 1/2 + 45
Total Area = 45.5 square units
The line Max(x, y) = 1 can be rewritten as two separate lines: x = 1 and y = 1.
To find the points of intersection, we substitute these equations into the equation of the circle:
x^2 + y^2 = 1
For x = 1, we have:
1^2 + y^2 = 1
y^2 = 0
y = 0
So, one point of intersection is (1, 0).
For y = 1, we have:
x^2 + 1^2 = 1
x^2 + 1 = 1
x^2 = 0
x = 0
So, another point of intersection is (0, 1).
Now, we have the two points of intersection: (1, 0) and (0, 1). These two points divide the circle into two segments.
To find the area of the bounded figure, we calculate the area of each segment and sum them.
The first segment is a triangle with base 1 and height 1 (formed by the points (1, 0), (0, 0), and (0, 1)). The area of a triangle is given by:
Area = (base * height) / 2
Area = (1 * 1) / 2
Area = 1/2
The second segment is a sector of the circle with radius 1 and central angle 90 degrees (formed by the points (0, 0), (1, 0), and (0, 1)). The area of a sector is given by:
Area = (radius^2 * angle) / 2
Area = (1^2 * 90) / 2
Area = 45
So, the total area of the bounded figure is:
Total Area = Area of Triangle + Area of Sector
Total Area = 1/2 + 45
Total Area = 45.5 square units
Free Test
FREE
| Start Free Test |
Community Answer
What is the area of a plane figure bounded by circle centered at orig...
Since x, y>0 thus we are talking of area in first quadrant only.
By definition the lines max, (x, y) = 1 means x = 1 and y £ 1 or y = 1 and x £ 1
Required area is shaded area as shown in the figure
= Area of square - Area of semicircle = 1 - (π/4) sq. units
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
What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer?
Question Description
What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. 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 What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer?.
What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. 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 What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer?.
Solutions for What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. 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 What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. 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