Question

the area of a sector of a circle is 44cm2,what is the radii of the cricle, if the angle at the centre is 140 ?​

Answer 1

$\red{\huge{\boxed{\tt{Question:-}}}}$

The area of a sector of a circle is 44cm², what is the radii of the circle if the angle at the center is 140°?​

$\pink{\huge{\boxed{\sf{Solution:-}}}}$

Area of sector = 44 cm²   (Given)

The angle at the center  = $\theta$ = 140°   (Given)

$\red{\underline{\underline{\sf{To\:\:be\:\:found:-}}}}$

The radius of the circle

The formula for the area of sector

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

Now,

$=\bf \dfrac{\theta}{360}\times \pi r^{2} \\ \\ \\ \implies \dfrac{14 \cancel{0} }{36 \cancel{0} }\times \dfrac{22}{7} \times r^{2}=44 \\ \\ \\ \implies \dfrac{14}{36} \times \dfrac{22}{7} \times r^{2}=44 \\ \\ \\ \implies \dfrac{\cancel{7}}{18} \times \dfrac{22}{\cancel{7}} \times r^{2} =44 \\ \\ \\ \big[ divide\: \:14 \:\:and\:\: 36 \:\:by\:\: 2\:\: \\ and\:\: divide \:\:22 \:\:and \:\:18 \:\:by \:\:2\big]$

$\bf \implies \dfrac{1}{9}\times \dfrac{11}{1} \times r^{2} = 44\\ \\ \\ \implies \dfrac{11}{9}\times r^{2} = 44 \\ \\ \\ \implies r^{2} = 44 \times \dfrac{9}{11}\\ \\ \\ \implies r^{2} = 4 \times 9 \\ \\ \\ \implies r^{2} = 36 \\ \\ \\ \implies r = \sqrt{36} \\ \\ \\ \implies r=6$

Hence,

Radius of circle = 6 cm.

Answer 2

✯✯ QUESTION ✯✯

The area of a sector of a circle is 44cm2,what is the radii of the cricle, if the angle at the centre is 140 ?

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\longmapsto\tt{Area\:Of\:Sector\:of\:Circle={44cm}^{2}}$

$\longmapsto\tt{Angle = 140}$

➥Using Formula : -

$\longmapsto\tt{\dfrac{\theta}{360}\times{\pi{{r}^{2}}}}$

➥Putting Values : -

$\longmapsto\tt{44=\dfrac{140}{360}\times\dfrac{22}{7}\times{{r}^{2}}}$

$\longmapsto\tt{44=\dfrac{\cancel{140}}{\cancel{360}}\times\dfrac{\cancel{22}}{\cancel{7}}}$

$\longmapsto\tt{\dfrac{44}{1}=\dfrac{11}{9}{r}^{2}}$

$\longmapsto\tt{{r}^{2}=\dfrac{9\times{\cancel{44}}}{\cancel{11}}}$

$\longmapsto\tt{{r}^{2}=9\times{4}}$

$\longmapsto\tt{{r}^{2}=\sqrt{36}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{r}\orange{=}\purple{6}}}$