Question

In Figure-8, a square OPQR is inscribed in a quadrant OAQB of a circle.
If the radius of circle is 62 cm, find the area of the shaded region.
Figure-​

Answer 1

Area of the shaded region is 1098.28 cm².

Step-by-step explanation:

OAQB is a quadrant of a circle and a square OPQR is inscribed in this quadrant.

Radius OA = OQ = 62 cm

OQ² = OP² + PQ² [By Pythagoras theorem]

OQ² = 2(OP)²

(62)² = 2(OP)²

OP = $\frac{62}{\sqrt{2}}$

OP = 31√2 cm

Area of the the shaded region = Area of the quadrant OAQB - Area of the square OPQR

= $\frac{\pi r^{2}}{4}-(OP)^{2}$ [Since area of OPQR = (Side)²]

= $\frac{\pi (62)^{2}}{4}-(31\sqrt{2})^{2}$

= $\frac{22\times (62)^{2}}{7\times 4}-1922$

= 3020.28 - 1922

= 1098.28 cm²

Therefore, area of the shaded region is 1098.28 cm².

Practice more questions to find the area from https://brainly.in/question/14461797

Answer 2

Answer:

area of quadrant = πr2÷4

(22÷7×62×62)÷4

(84568÷7)×(1÷4)

84568÷28

3020.28 cm2

let side of square = x

diagonal of square=√2×side

r = √2× x

x=r÷2 = 62÷√2cm

area of square = S×S