Question

find the area of a quadrant of a circle whose circumference is equal to 22 CM​

Answer 1

Open the image to see the propriate written answer

Answer 2

Given:-

• Circumference of the quadrant = 22cm

To Find:-

• Area of the given quadrant

Concept:-

• Firstly we have to understand the concept.Circumference of the quadrant is given and we have to find the radius first by substituting the values in the equation clearly.Secondly,we have to find the area of the quadrant by substituting the values in the equation to find the area.

Formulae Applied:-

$\</u></strong><strong><u>L</u></strong><strong><u>arge</u></strong><strong><u>\</u></strong><strong><u>b</u></strong><strong><u>o</u></strong><strong><u>x</u></strong><strong><u>e</u></strong><strong><u>d</u></strong><strong><u>{</u></strong><strong><u>\</u></strong><strong><u>s</u></strong><strong><u>f</u></strong><strong><u>{</u></strong><strong><u>C</u></strong><strong><u>ircumference</u></strong><strong><u> \: of \: a \: </u></strong><strong><u>Q</u></strong><strong><u>uadrant \: = \: 2\pi r}</u></strong><strong><u>}</u></strong><strong><u>$

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

Solution:-

First,find the radius by substituting the given values.

$\Large\boxed{\sf{Circumference \: of \: the\: Quadrant \: = \: 2\pi r}}$

$\implies\large\sf{2\pi r \: = \: 22cm}$

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

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

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

$\implies\large\sf{r \: = \: \frac{154}{44} \: = \:3.5}$

$\implies\large\sf{r \: = \:3.5cm}$

We got the radius as 3.5cm.

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Now,find the area of the quadrant by substituting all the values.

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

$\implies\large\sf{\frac{1}{4} \: \times \: \frac{22}{7} \: \times \: (3.5) \: \times \: (3.5)}$

$\implies\large\sf{\frac{1}{2} \: \times \: \frac{11}{2} \: \times \: 3.5}$

$\implies\large\sf{\frac{11}{4}\: \times \: 3.5}$

$\implies\large\sf{9.625cm}$

Hence,we got the Area of the Quadrant as 9.625cm.

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