Question

find area of quadrant of a circle whose circumference is 22cm​

Answer 1

Answer:

9.625cm

Step-by-step explanation:

we have

C=22cm

⇒2πr=22cm

⇒2×

7

22

×r=22

∴r=3.5cm

Now,

area of quadrantofacircle=

4πr2=7

22× 4(3.5) 2= 28

22×12.25 = 9.625cm

.

Answer 2

$\sf \underline{ \large{Given - }}$

$\sf \dashrightarrow \: Circumference \: of \: the \: circle = 22 \: cm$

$\sf \underline{ \large{To \: find - }}$

$\sf \dashrightarrow \: The \: area \: of \: quadrant \: of \: a \: circle = \: ?$

$\sf \underline{ \large{Solution - }}$

$\sf \dashrightarrow \underline{\boxed{ \sf Area \: of \: Quadrant = \dfrac{1}{4} \pi {r}^{2} }}$

$\bf Now,$

$\sf \dashrightarrow Circference \: of \: a \: circle = 22 \: cm$

$\sf \dashrightarrow 2 \pi r =22$

$\sf \dashrightarrow 2 \times \dfrac{22}{7} \times r =22$

$\sf \dashrightarrow r = \dfrac{ \!\!\!\not2\!\!\!\not2 \times 7}{ \: \!\!\!\not2\!\!\!\not2 \times 2}$

$\sf \dashrightarrow r = \dfrac{ 7}{ 2}$

$\sf \dashrightarrow r = 3.5 \: cm$

$\bf \underline{ Now},$

$\sf \dashrightarrow \ \sf Area \: of \: Quadrant = \dfrac{1}{4} \pi {r}^{2}$

$\sf \dashrightarrow \ \sf \dfrac{1}{4} \times \dfrac{22}{7} \times (3.5)^{2}$

$\sf \dashrightarrow \ \sf \dfrac{1}{4} \times \dfrac{22}{7} \times 12.25$

$\sf \dashrightarrow \ \sf \dfrac{\!\!\!\not2\!\!\!\not2 \times 12.25}{\!\!\!\not4 \times 7}$

$\sf \dashrightarrow \ \sf \dfrac{11 \times 12.25}{2 \times 7}$

$\sf \dashrightarrow \ \sf \dfrac{134.75}{14}$

$\sf \dashrightarrow \ \sf 9.625$

$\bf Hence,$

$\sf \dashrightarrow \: \underline{\boxed{ \sf The\: area \: of \: quadrant \: of \: a\:circle\: is \: 9.625 \: cm^{2} }}$