CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number – 30/5/1
Question Number – 34
square OPQR is inscribed in a quadrant
area of the shaded region
quadrant of a circle
Deepak BoraNewbie
In the given figure, a square OPQR is inscribed in a quadrant OAQB of a circle. If the radius of circle is 6 √2 cm, find the area of the shaded region.
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Given,
Radius of circle r = 6 √2
OA = OB = OQ =6 √2 cm
In Δ OPQ,
(OP)² + (PQ)² = (OQ)²
2(OP)² = (6 √2)²
a = op = 6 cm
Area of the shaded region = ar (quadrant, with r = (6 √2) – ar (square with side 6 cm)
= [1/4 (𝜋 × r²] − 𝑎²
= [1/4 ( 3.14 × (6√2)² ) ] − 6²
= [18 𝑥 3.14] − 36
= 56.52 − 36
= 20.52 cm²
∴ the area of the shaded region is 20.52 cm²