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In an adjoining figure acb is the quadrant with radius a a semicircle is drawn outside the quadrant taking ab as a diameter. Find the area of shaded region?
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In an adjoining figure acb is the quadrant with radius a a semicircle ...
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In an adjoining figure acb is the quadrant with radius a a semicircle ...
Problem: 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 the shaded region.
Solution:
To find the area of the shaded region, we need to subtract the area of the quadrant from the area of the semicircle.
Step 1: Calculate the area of the quadrant:
The area of a quadrant is given by one-fourth of the area of the circle. Since the radius of the quadrant is a, the area of the quadrant is:
A = (1/4) * π * a^2
Step 2: Calculate the area of the semicircle:
The area of a semicircle is given by half of the area of the circle. Since the radius of the semicircle is also a, the area of the semicircle is:
A = (1/2) * π * a^2
Step 3: Subtract the area of the quadrant from the area of the semicircle:
To find the area of the shaded region, we subtract the area of the quadrant from the area of the semicircle:
Shaded Area = Area of Semicircle - Area of Quadrant
Shaded Area = [(1/2) * π * a^2] - [(1/4) * π * a^2]
Step 4: Simplify the expression:
To simplify the expression, we need to find a common denominator for the fractions:
Shaded Area = [(2/4) * π * a^2] - [(1/4) * π * a^2]
Shaded Area = [(2 - 1)/4] * π * a^2
Shaded Area = (1/4) * π * a^2
Step 5: Final Answer:
The area of the shaded region is (1/4) * π * a^2.
Solution:
To find the area of the shaded region, we need to subtract the area of the quadrant from the area of the semicircle.
Step 1: Calculate the area of the quadrant:
The area of a quadrant is given by one-fourth of the area of the circle. Since the radius of the quadrant is a, the area of the quadrant is:
A = (1/4) * π * a^2
Step 2: Calculate the area of the semicircle:
The area of a semicircle is given by half of the area of the circle. Since the radius of the semicircle is also a, the area of the semicircle is:
A = (1/2) * π * a^2
Step 3: Subtract the area of the quadrant from the area of the semicircle:
To find the area of the shaded region, we subtract the area of the quadrant from the area of the semicircle:
Shaded Area = Area of Semicircle - Area of Quadrant
Shaded Area = [(1/2) * π * a^2] - [(1/4) * π * a^2]
Step 4: Simplify the expression:
To simplify the expression, we need to find a common denominator for the fractions:
Shaded Area = [(2/4) * π * a^2] - [(1/4) * π * a^2]
Shaded Area = [(2 - 1)/4] * π * a^2
Shaded Area = (1/4) * π * a^2
Step 5: Final Answer:
The area of the shaded region is (1/4) * π * a^2.
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In an adjoining figure acb is the quadrant with radius a a semicircle is drawn outside the quadrant taking ab as a diameter. Find the area of shaded region?
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In an adjoining figure acb is the quadrant with radius a a semicircle is drawn outside the quadrant taking ab as a diameter. Find the area of 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 In an adjoining figure acb is the quadrant with radius a a semicircle is drawn outside the quadrant taking ab as a diameter. Find the area of shaded region? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an adjoining figure acb is the quadrant with radius a a semicircle is drawn outside the quadrant taking ab as a diameter. Find the area of shaded region?.
In an adjoining figure acb is the quadrant with radius a a semicircle is drawn outside the quadrant taking ab as a diameter. Find the area of 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 In an adjoining figure acb is the quadrant with radius a a semicircle is drawn outside the quadrant taking ab as a diameter. Find the area of shaded region? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an adjoining figure acb is the quadrant with radius a a semicircle is drawn outside the quadrant taking ab as a diameter. Find the area of shaded region?.
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