Answer:
Let l be the length of an ac and r be the radius of the circle.
Use the fact that the length of an arc intercepted by an angle is proportional to the radius
i.e
[tex]l \propto r[/tex]
⇒[tex]l = r \theta[/tex] where, [tex]\theta[/tex] is the angle in radian.
To find the Area of the sector:
Given: r = 3 cm and [tex]\theta = \frac{\pi}{4}[/tex]
[tex]\text{Area of the sector A} = \pi r^2 \cdot \frac{\theta}{360^{\circ}}[/tex]
where, [tex]\theta[/tex] is the angle in degree.
Use conversion:
1 radian = [tex]\frac{180}{\pi}[/tex] degree
then;
[tex]\frac{\pi}{4}[/tex] = [tex]\frac{\pi}{4 } \times \frac{180}{\pi} = 45^{\circ}[/tex]
then;
[tex]\theta =45^{\circ}[/tex] and use [tex]\pi = 3.14[/tex]
Substitute the given values we have;
[tex]A= 3.14 \cdot 3^2 \cdot \frac{45}{360}[/tex]
⇒[tex]A = 3.14 \cdot 9 \cdot 0.125[/tex]
Simplify:
[tex]A = 3.5325[/tex] square cm
Therefore, the area of the sector is, 3.5325 square cm
