Question

2. Find the area of a quadrant of a circle whose circumference is 22 cm.
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Answer 1

Answer:

0.0795

Step-by-step explanation:

$circumfurence = \pi d\\\\radius=0.318area of a quadrant = \pi r^{2} /4 (since quadrant is 1/4)\\so area=\frac{\pi 0.318^{2} }{4} = 0.0795$

Answer 2

Given :-

• Circumference = 22 cm

To find :-

• The area of quadrant of circle

Solution :-

we know that, one fourth of a circular disc is called a quadrant.

• The central angle of a quadrant is 90°

so,

• Angle (θ) = 90°

Now,

Circumference of circle = 22 cm

⤇ 2πr = 22

$\rm\:\longrightarrow\:2\times\dfrac{22}{7}\times{r}=22$

$\rm\longrightarrow\dfrac{44}{7}\times{r}=22$

$\rm\longrightarrow\:r=\dfrac{22}{\dfrac{44}{7}}$

$\rm\longrightarrow\:r=\cancel{22}\times\dfrac{7}{\cancel{44}}$

$\rm\longrightarrow\:r=\dfrac{7}{2}$

Then,

we know that,

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\red{Area\:of\:quadrant=\dfrac{\theta}{360\degree}\times{\pi}{r}^{2}}}}}$

$\rm\longrightarrow\:Area=\dfrac{90\degree}{360\degree}\times\dfrac{22}{7}\times\bigg(\dfrac{7}{2}\bigg)^2$

$\rm\longrightarrow\:Area=\dfrac{9}{36}\times\dfrac{\cancel{22}}{\cancel{7}}\times\dfrac{\cancel{7}}{\cancel{2}}\times\dfrac{7}{2}$

$\rm\longrightarrow\:Area=\dfrac{\cancel{693}}{\cancel{72}}$

$\rm\longrightarrow\:Area=\dfrac{77}{8}\:{cm}^{2}$

Hence,the area of quadrant of circle will be 77/8 cm².