CUET Preparation Today
CUET
General Test
Quantitative Reasoning
Mensuration: 2D
PQR is a quadrant whose radius is 7 cm. A circle is inscribed in the quadrant. What is the area of the circle(in cm²)? |
154 (3 - 2√2) 308 (3 - 2√2) 308 (3 + 2√2) 154 (3 + 2√2) |
154 (3 - 2√2) |
QR = 7 cm., QT = x cm, OT = OU = r cm, QU = QO + OU = 2r + x = 7cm. ............(i) OQ = √QS2+OS2 = √r2+r2 ⇒ x + r = √2r ⇒ x = (√2 - 1) r From (i) 2r + (√2 - 1) r = 7 r (√2 + 1) = 7 r = 7√2+1 = 7 (√2 - 1) ⇒ Area of Circle = π r2 = 227 × 7 × 7 (√2 - 1)2 = 154 (2 + 1 - 2√2) =154 (3 - 2√2) |