Question

Find the area of quadrant of circle whose circumference is 22cm​

Answer 1

$\sf{\underline{Here:}}$

We have to find the circumference (circle) and then the area of a quadrant.

$\sf{\underline{Formulas\:to\:be\:used:}}$

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

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

$\sf{\underline{Circumference:}}$

$\implies$ $\sf{2\pi r}$

$\implies$ $\sf{22 = 2 \times \frac{22}{7} \times r}$

$\implies$ $\sf{r = \frac{22 \times 7}{22 \times 2}}$

$\implies$ $\sf{r = \frac{154}{44}}$

$\implies$ $\boxed{\sf{r = 3.5}}$

$\sf{\underline{Now:}}$

$\sf{\underline{Area\:of\:a\:quadrant:}}$

$\implies$ $\sf{ \frac{1}{4} \pi {r}^{2}}$

$\implies$ $\sf{\frac{1}{4} \times \frac{22}{7} \times 3.5 \times 3.5}$

$\implies$ $\sf{ \frac{1 \times 22 \times 35 \times 35}{4 \times 7 \times 10 \times 10}}$

$\implies$ $\sf{\frac{1 \times 11 \times35 }{4 \times 10}}$

$\implies$ $\sf{ \frac{385}{40}}$

$\implies$ $\boxed{\sf{9.625 \: {cm}^{2}}}$

$\sf{\underline{Therefore:}}$

The area of quadrant of circle is $\sf{9.625 \: {cm}^{2}}$.

Answer 2

$\huge\star{\red{\underline{\mathfrak{Answer :-}}}}$

$\implies {\frac{77}{8} {cm}^{2}}$

$\huge\star{\red{\underline{\mathfrak{Explanation :-}}}}$

Given :-

The circumference of the circle is 22 cm.

To find :-

The area of a quadrant of the circle.

Solution :-

If the circumference = 22 cm.

Then,

$\leadsto {2\pi \: r = 22 \: cm}$

$\leadsto {2 \times \frac{22}{7} \times r = 22}$

$\leadsto {r = 22 \times \frac{7}{22} \times \frac{1}{2} }$

$\leadsto {r = \frac{7}{2}}$

Therefore, radius of the circle = 7/2 cm

Now, let us find the area of the quadrant of the circle.

The formula to find the area of the quadrant of the circle is :- $\frac{\pi {r}^{2} }{4}$

So, putting in the values that we know :-

$= \frac{ \frac{22}{7} \times ( { \frac{7}{2} )}^{2} }{4}$

$= \frac{11\:\:\cancel {22} }{\cancel {7}} \times \frac {\cancel {7}}{2} \times \frac{7}{2} \times \frac{1}{\cancel{4} \:\: 2}$

$= \frac{11 \times 7}{2 \times 2 \times 2}$

$= \frac{77}{8} {cm}^{2}$

So, the area of the quadrant of the circle is : (77/8) cm^2.

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