A sector of angle 125° is revomed from a thin circular sheet of radius 18cm. it is then folded with straight edges coinciding to form a right circular cone. what are the steps you would use to calculate the base radius, the semi - vertical, and the volume of the cone?

Volume of the cone is 1883.7 cm³

Step-by-step explanation:

The circumference of the full circle with radius 18 cm:

360 : = 2*π*18 = 36π cm

125 : = 125/360 * 36π

The new circumference is maller:

36π - 125/360 * 36π

36π * 0.652 (7)

Calculate the new r based on the new circomference:

2*π * r = 36π * 0.652 (7)

r = 36π/2π * 0.652 (7)

r = 18 * 0.652 (7)

r = 11.75 cm

Based on this radius you can calculate the area of the base of the cone.

area base = π * (11.75) ²

The Volume V of this cone = 1/3 π r² * h

You can calculate the height h by using Pythagoras theorum.

The sector is the hypothenusa = 18 cm

The h is the height, which is the "unknown"

The r is the new radius = 11.75 cm

s² = r² + h²

h² = s² - r²

h = √ (s² - r²)

h = √ (18² - 11.75²)

h = 13.6358901432946 cm

h = 13.636 cm

V cone

V = 1/3 π 11.75² * h

V = 1/3 π 11.75² * √ (18² - 11.75²)

V = 1/3 π 11.75² * 13.636

V = 1883.7 cm³