In the figure given below, O is the centre of the circle. PR and RQ are chords of the circle. The radius of the circle is 5 cm. PR = 8 cm, QR = 6 cm and ∠PRQ = 90°. What is the approximate area of the shaded region? A. ( 25 4 π − 24 ) cm2 B. ( 25 2 π − 24 ) cm2 C. ( 25 4 π) cm2 D. ( 25 2 π) cm2 5. Shown below are the graphs of the lines − 2
Answers
Step-by-step explanation:
Correct option is (B) ( 25/2 π − 24 ) cm2
Approximate area of the shaded region is (25π/2 - 24) cm²
Given:
- A Circle with center O
- PR and RQ are chords of the circle
- The radius of the circle is 5 cm.
- PR = 8 cm, QR = 6 cm , ∠PRQ = 90°.
To Find:
- Approximate area of the shaded region
Solution:
Area of a circle = π (Radius)²
Area of a semicircle = (1/2) π (Radius)²
Area of a right angle triangle = (1/2) x base x perpendicular
Step 1:
Calculate Area of semicircle using radius = 5 cm
Area of semicircle = (1/2) π (5)²
Area of semicircle = 25π/2
Step 2:
Calculate Area of right triangle PQR by substituting PR = 8 , QR = 6 cm
Area of ΔPQR = (1/2) x PR x QR
Area of ΔPQR = (1/2) x 8 x 6
Area of ΔPQR = 24
Step 3:
Calculate Area of Shaded region by subtracting area of triangle PQR from area of semicircle
Area of the shaded region = (25π/2 - 24) cm²
Correct option is B) (25π/2 - 24) cm²
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