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In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadrant
taking AB as a diameter. Find the area of shaded region can not be :?
taking AB as a diameter. Find the area of shaded region can not be :?
Most Upvoted Answer
In the adjoining figure ACB is a quadrant with radius 'a'. A semicircl...
Problem Statement:
In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadrant taking AB as a diameter. Find the area of shaded region can not be :? Explain in details.
Solution:
Let's first identify the shaded region in the given figure:
The shaded region is the area between the quadrant ACB and the semicircle ADB.
Step 1: Find the Area of the Quadrant ACB
The area of a quadrant of a circle with radius 'a' is given by:
Area of Quadrant ACB = 1/4 * π * a²
Step 2: Find the Area of the Semicircle ADB
The area of a semicircle with diameter 'd' is given by:
Area of Semicircle ADB = 1/2 * π * (AB/2)²
Here, AB is the diameter of the semicircle and is equal to the radius of the quadrant, which is 'a'.
Therefore, the area of the semicircle ADB is:
Area of Semicircle ADB = 1/2 * π * (a/2)² = πa²/8
Step 3: Find the Required Area of the Shaded Region
To find the area of the shaded region, we need to subtract the area of the semicircle ADB from the area of the quadrant ACB:
Required Area of Shaded Region = Area of Quadrant ACB - Area of Semicircle ADB
Required Area of Shaded Region = 1/4 * π * a² - πa²/8
Required Area of Shaded Region = 2πa²/8 - πa²/8
Required Area of Shaded Region = πa²/8
Final Answer:
Therefore, the area of the shaded region is given by πa²/8.
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In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadranttaking AB as a diameter. Find the area of shaded region can not be :?
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In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadranttaking AB as a diameter. Find the area of shaded region can not be :? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadranttaking AB as a diameter. Find the area of shaded region can not be :? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadranttaking AB as a diameter. Find the area of shaded region can not be :?.
In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadranttaking AB as a diameter. Find the area of shaded region can not be :? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadranttaking AB as a diameter. Find the area of shaded region can not be :? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadranttaking AB as a diameter. Find the area of shaded region can not be :?.
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