Question

8. PQ is the diameter of the semicircle with
centre O. OR is the diameter of the small
circle inscribed in it. Find the shaded area if
PQ = 21 cm.​

Answer 1

Given :

• Diameter of semi-circle = PQ = 21cm
• Diameter of small circle = OR = Radius of semi-circle

To find : Area of shaded region

Formula used :

• Area of circle = πr²
• Area of semi-circle = (πr²)/2

Method used :

Find area of semi-circle , and subtract area of small circle from it . It will give area of shaded region

Solution :

Radius of semi-circle = 21/2 cm

Radius of small circle = (21/2) ÷ 2 = 21/4 cm

Area of semi-circle = {π ×(21/2)² } ÷ 2

Area of semi-circle = π × (21)² / 8 cm²

Area of small circle = π (21/4)²

Area of small circle = π (21²) /16

Area of shaded region = Area of semi-circle - Area of small circle

Area of shaded region =

$\sf \: \dfrac{\pi ({21}^{2}) }{8} - \dfrac{\pi( {21}^{2} )}{16} \\ \\ \implies \sf \: \dfrac{\pi( {21}^{2}) }{8} (1 - \dfrac{1}{2} ) \\ \\ \implies \sf \: \dfrac{22}{7} \times \dfrac{441}{8} \times \dfrac{1}{2} \\ \\ \implies \sf \: \frac{693}{8} {cm}^{2} \\ \\ \implies \sf \: 86.625 \: {cm}^{2}$

ANSWER :

• Area of shaded region = (693/8)cm² = 86.625 cm²