Final answer:
To find the sectoral angle, use the formula (Area * 360) / (π * r^2). The perimeter of the sector is calculated using the circumference and arc length. The volume of the cone formed can be found using the formula (1/3) * π * r^2 * h.
Step-by-step explanation:
To find the sectoral angle, we can use the formula for the area of a sector: Area = (θ/360)πr^2, where θ is the angle in degrees and r is the radius. Rearranging the formula, we have θ = (Area * 360) / (π * r^2). Substitute the given values to find θ.
For the perimeter of the sector, we need to find the circumference of the circle and then calculate the arc length based on the sectoral angle. Perimeter = (2 * π * r) + (θ/360) * (2 * π * r).
The volume of the cone formed when the sector is bent is given by V = (1/3) * π * r^2 * h, where r is the radius of the circle and h is the perpendicular distance between the center of the circle and the sector. Substitute the given values to find the volume.