To find the curved surface area and volume of the cone formed by rolling a sector of radius 36 cm and central angle 150°, let's break it down step-by-step.

Step 1: Curved Surface Area of the Cone

The radius of the sector represents the slant height (l) of the cone, which is given as 36 cm.

The arc length of the sector forms the circumference of the base of the cone. The formula for the arc length is: $\text{Arc Length} = \frac{\theta}{360^\circ} \times 2 \pi r$ Where:

• $\theta = 150^\circ$ (central angle)
• (r =