Class 10 Exam > Class 10 Questions > Abcd is a square,inside which 4 circles with ...
Start Learning for Free
Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region?
Most Upvoted Answer
Abcd is a square,inside which 4 circles with radius 1 cm each are touc...
Problem:
ABCD is a square, inside which 4 circles with radius 1 cm each are touching each other. What is the area of the shaded region?
Solution:
To solve this problem, we need to follow these steps:
Step 1:
Draw the diagram of the given problem.
Step 2:
Find the area of the square.
Since all sides of the square are equal and given as 2 cm in the problem,
Area of the square = (Side)^2 = (2)^2 = 4 cm^2.
Step 3:
Find the radius of the circle which is inscribed in the square.
The diagonal of the square is equal to the diameter of the circle.
Diagonal of the square = 2√2 cm
Diameter of the circle = Diagonal of the square = 2√2 cm
Radius of the circle = Diameter/2 = (√2) cm
Step 4:
Find the area of one circle.
Area of one circle = πr^2 = π(1)^2 = π cm^2.
Step 5:
Find the area of the shaded region.
Area of the shaded region = Area of the square – 4(Area of one circle)
Area of the shaded region = 4 cm^2 – 4(π cm^2)
Area of the shaded region = 4 cm^2 – 4π cm^2
Area of the shaded region = 4(1 – π) cm^2
Therefore, the area of the shaded region is 4(1 – π) cm^2.
ABCD is a square, inside which 4 circles with radius 1 cm each are touching each other. What is the area of the shaded region?
Solution:
To solve this problem, we need to follow these steps:
Step 1:
Draw the diagram of the given problem.
Step 2:
Find the area of the square.
Since all sides of the square are equal and given as 2 cm in the problem,
Area of the square = (Side)^2 = (2)^2 = 4 cm^2.
Step 3:
Find the radius of the circle which is inscribed in the square.
The diagonal of the square is equal to the diameter of the circle.
Diagonal of the square = 2√2 cm
Diameter of the circle = Diagonal of the square = 2√2 cm
Radius of the circle = Diameter/2 = (√2) cm
Step 4:
Find the area of one circle.
Area of one circle = πr^2 = π(1)^2 = π cm^2.
Step 5:
Find the area of the shaded region.
Area of the shaded region = Area of the square – 4(Area of one circle)
Area of the shaded region = 4 cm^2 – 4(π cm^2)
Area of the shaded region = 4 cm^2 – 4π cm^2
Area of the shaded region = 4(1 – π) cm^2
Therefore, the area of the shaded region is 4(1 – π) cm^2.
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
Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region?
Question Description
Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? 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 Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region?.
Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? 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 Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region?.
Solutions for Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? 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 Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? defined & explained in the simplest way possible. Besides giving the explanation of
Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region?, a detailed solution for Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? has been provided alongside types of Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? theory, EduRev gives you an
ample number of questions to practice Abcd is a square,inside which 4 circles with radius 1 cm each are touching each other.what is the area of the shaded region? 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