If in a circle of radius r = 36 cm a sector of arc length l, satisfies 4l =3r, then the area of the sector is:

Correct option is B

Given:

Radius of the circle, r = 36cm

Arc length of the sector is  l and  satisfies 4l = 3r

Formula Used:

Arc length formula: $$l = \theta \cdot r \quad \text{(where $ \theta $ is in radians)}$$​ 

Area of a sector formula:$$A = \frac{1}{2} \cdot r^2 \cdot \theta$$​ 

Solution:

4l = 3r

$$l = \frac{3r}{4} = \frac{3 \cdot 36}{4} = 27 \, \text{cm}.$$

$$\theta = \frac{l}{r} = \frac{27}{36} = \frac{3}{4} \, \text{radians}.$$

$$A = \frac{1}{2} \cdot r^2 \cdot \theta = \frac{1}{2} \cdot 36^2 \cdot \frac{3}{4} = 486 \, \text{cm}^2.$$​​

Thus area of the sector is 486 cm².