Question

The area of a circle with radius 6cm with angle of the sector is [60]^0 is

Answer 1

Question :–

• The area of a circle with radius 6cm with angle of the sector is 60⁰ is ?

ANSWER :–

GIVEN :–

• Radius of circle is 6cm.

• Angle of the sector is 60⁰.

TO FIND :–

• Area of sector = ?

SOLUTION :–

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\qbezier(-32.5,0)(-32.5,29.5)(0,31.5)\qbezier(0,31.5)(31.5,29.5)(32.5,0)\qbezier(32.5,0)(31.5,-29.5)(0,-31.5)\qbezier(0,-31.5)(-31.5,-29.5)(-32.5,0)\put(0,0){\line(-1,-2){14.5}}\put(0,0){\line(1,-2){14.5}}\footnotesize\put(-1.5,1){O}\put(-18,-31){A}\put(16,-31){B}\put(-14.5,-28.6){\line(1,0){29}}\qbezier(-2,-4)(0,-5)(2,-4)\put(-2.3,-8.7){ 60^{\circ} }\put(-1.5,-35.3){C}\put(-15.5,-13.5){6\ cm}\end{picture}$

• We know that –

$\\ \large{ \huge{ \star}} \: \: \: { \red{ \boxed{ \bold{Area \: \: of \: \: sector = \frac{ \theta}{360^{ \circ} } \times \pi {r}^{2} }}}}$

• Now put the values –

$\\ \implies { \bold{Area \: \: of \: \: sector = \frac{60^{ \circ}}{360^{ \circ} } \times \pi {(6)}^{2} }}$

$\\ \implies { \bold{Area \: \: of \: \: sector = \frac{ \cancel{60^{ \circ}}}{ \cancel{360^{ \circ} }} \times \pi \times \cancel6 \times 6 }}$

$\\ \implies { \bold{Area \: \: of \: \: sector = 6 \pi }}$

$\\ \implies { \bold{Area \: \: of \: \: sector = 6 \times \dfrac{22}{7} \: \: \: [ \: \because \: \: \pi \: = \dfrac{22}{7} ] }}$

$\\ \implies { \bold{Area \: \: of \: \: sector = \dfrac{132}{7} \: \: }}$

$\\ \implies \large{ \pink{ \boxed{ \bold{Area \: \: of \: \: sector = 18.86 \: \: cm ^{2} \: \: }}}}$