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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?
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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.
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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?
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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?.
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