Question

find the area of shaded region​

Answer 1

Answer:

θ = π/2

Area of sector = 1/2 r² θ

= 1/2 r² π/2

= πr²/4

Area of circle = πr²

Area of shaded region

= πr²/4 - πr²

= (πr² - 4πr²)/4

= -3πr²/4 sq unit,,

Answer 2

Question:

Find the area of shaded region.

Answer:

$Area \: of \: shaded \: region \: is \: \underline{ \: \underline{ \: \sf \pink{101.8 \: sq.units} \: } \: }$

Given:

★ A diagram is given,

• A Circle is fixed in the quadrant.

$\bigstar Radius \: of \: quadrant = 12cm$

$\bigstar Radius \: of \: circle = ?$

Step-by-step explanation:

We know that,

$\boxed{Area \: of \: quadrant = \frac{1}{4} \pi {r}^{2} \: sq.units }$

$Let \: the \: value \: of \: \underline{ \: \underline{ \: \bold{\pi \: be \: \frac{22}{7}} \: } \: }$

$\implies \frac{1}{ \not{4}} \times \frac{22}{7} \times \not{12}_{3} \times 12$

$\implies \frac{22 \times 3 \times 12}{7}$

$\implies \frac{792}{7}$

$\implies \boxed{113.14 \: sq.units}$

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\boxed{Circumference = 2 \pi r }$

$\mapsto 2\pi r = 12$

$\mapsto \boxed{\pi r = 6}$

$\mapsto \frac{22}{7} \times r = 6$

$\mapsto r = 6 \times \frac{7}{22}$

$\mapsto \boxed{ r = 1.90}$

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}$

$\boxed{Area \: of \: circle = \pi {r}^{2} \: sq.units }$

$\hookrightarrow (\pi r)r$

$\hookrightarrow 6(1.9)$

$\hookrightarrow \boxed{ 11.4 \: sq.units}$

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\bigstar Area \: of \: shaded \: region$

$\longrightarrow Area \: of \: quadrant - Area \: of \: circle$

$\longrightarrow 113.14 - 11.34$

$\longrightarrow \boxed{101.8 \: sq.units}$

$\therefore Area \: of \: shaded \: region \: is \: \underline{ \: \bold{101.8 \: sq.units} \: }$

Formula used:

$\bigstar Area \: of \: quadrant = \frac{1}{4} \pi {r}^{2} \: sq.units$

$\bigstar Circumference = 2 \pi r$

$\bigstar Area \: of \: circle = \pi {r}^{2} \: sq.units$