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
\(l \propto r\)
⇒\(l = r \theta\) where, \(\theta\) is the angle in radian.
To find the Area of the sector:
Given: r = 3 cm and \(\theta = \frac{\pi}{4}\)
\(\text{Area of the sector A} = \pi r^2 \cdot \frac{\theta}{360^{\circ}}\)
where, \(\theta\) is the angle in degree.
Use conversion:
1 radian = \(\frac{180}{\pi}\) degree
then;
\(\frac{\pi}{4}\) = \(\frac{\pi}{4 } \times \frac{180}{\pi} = 45^{\circ}\)
then;
\(\theta =45^{\circ}\) and use \(\pi = 3.14\)
Substitute the given values we have;
\(A= 3.14 \cdot 3^2 \cdot \frac{45}{360}\)
⇒\(A = 3.14 \cdot 9 \cdot 0.125\)
Simplify:
\(A = 3.5325\) square cm
Therefore, the area of the sector is, 3.5325 square cm
