Question

the area of a sector and the length of the arc of the sector aur equal in numerical value then the radius of the circle is​

Answer 1

GIVEN:

• The area of a sector and the length of the arc of the sector aur equal in numerical value.

TO FIND:

• What is the radius of the circle ?

SOLUTION:

We have given that, the area of a sector and the length of the arc of the sector aur equal in numerical value

We have to find the radius of the circle

We know that the formula for finding the area of Sector is:-

$\Large{\boxed{\bf{\star \: AREA = \dfrac{\theta}{360\degree} \times \pi r^2 }}}$

To find the length of the arc, we use the formula:-

$\Large{\boxed{\bf{\star \: LENGTH = \dfrac{\theta}{360\degree} \times 2 \pi r\: \star}}}$

According to given conditions:-

$\bf{ \dfrac{\theta}{360\degree} \times \pi r^2 = \dfrac{\theta}{360\degree} \times 2 \pi r}$

$\rm{\dashrightarrow \cancel\dfrac{\theta}{360\degree} \times \cancel{\pi} r^2 = \cancel\dfrac{\theta}{360\degree} \times 2 \cancel{\pi} r }$

$\rm{\dashrightarrow r^2 = 2r }$

$\rm{\dashrightarrow \cancel{r^2} = 2\cancel{r} }$

$\bf{\dashrightarrow r = 2 \: cm}$

❝ Hence, the radius of the circle is 2 cm ❞

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