Question

In Fig.15.70, OACB is a quadrant of a circle with centre O and radius 3.5cm. If OD=2cm, find the area of the (i) quadrant OACB (ii) shaded region.

Answer 1

Step-by-step explanation:

(i) Area of quadrant OACB = πr²/4

=> (22/7×1/4)× 3.5²

=> (3.14×0.25) × 12.25

=> 0.7857 × 12.25

=> 9.624 cm²

(ii) Area of shaded region = 1/4 × π(R² – r²)

=> 0.25 × 3.14 ×(3.5² – 2²)

=> 0.785 × (12.25 – 4)

=> 0.785 × 8.25

=> 6.476 cm²

Answer 2

$\huge{\underline{\bigstar{\sf{solution!!}}}}$

Given,OACB is a quadrant of a circle

Radius = 3.5 =7/2 cm; OD= 2cm

$\large{\sf{area\: of \: the \: shaded \: region = area \: of \: a \: quadrant \: cricle - area \:of \: triangle \:BOB}}$

=1/4πr²-1/2×b×h

=1/4×22/7×7/2×7/2-1/2×7/2×2

=11×7/2×2×2 -7/2

[=77/8-7/2

=9.625-3.5

$\large{\boxed{\sf{=6.125cm2}}}$

━━━━━━━━━━━━━━━━━━━━