Question

Find the area of the shaded part of
the figure if the diameter of the
outer circle is 20 cm and the radius of
the inner circle is 6 cm.​

Answer 1

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find the area of shaded region.

$\huge\bf\underline \red{ \mathcal{S}olution:-}$

$\bf\underline{\purple{Given:-}}$

• Diameter of outer circle = 20cm
• Radius of inner circle = 6cm

We know that,

• Area of circle = πr²

• Radius of outer circle = D/2

⠀

= 20/2

= 10 cm

• Finding Area of outer circle :-⠀

⇛ Area of outer circle = π × 10 × 10

⇛ Area of outer circle =100π cm²

• Finding area of inner circle :-⠀

• Radius of inner circle = 6cm

⇛ Area of inner circle = π × 6 × 6

⇛ Area of inner circle = 36π cm²

⠀

• Area of shaded region = Area of outer circle - Area of inner circle/2

⠀

⇛Area of shaded region = 100π - 36π/2

⇛Area of shaded region = 100π - 18π

⇛Area of shaded region = 82π

⇛Area of shaded region = 82 × 22/7

Hence,

• Area of shaded region = 257.714 cm²

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Given :-

• Diameter of outer circle = 20cm
• Radius of inner circle = 6cm

SOLUTION :-

• Radius of outer circle = 20/2 = 10cm

We know,

• Area of circle = $\sf πr^{2}$

Shaded region = Area of outer - Area of inner circle/2

Shaded region→ 22/7 × 10 × 10 - 22/7 × 6 × 6/2

Shaded region→ 3.1428 × 100 - 3.14 × 36/2

Shaded region→ 314.28 - 3.1428 × 18

Shaded region→ 314.28 - 56.570

Shaded region→ 257. 709

Hence,

• Area of shaded region = 257. 709 sq.cm