Question

A sector of angle 125° is revoked 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?​

Answer 1

Answer:

Step-by-step explanation:

A sector is a portion of the circle that is bounded by 2 radii forming an angle at the center of the circle. If it is folded into a cone, the radius of the sector becomes the slant height of the cone. The length of the arc formed by the sector becomes the circumference of the circular base of the cone. Therefore, to calculate the

1) Base radius, we would apply the formula,

Circumference = 2πr

Circumference = length of arc = 125/360 × 2 × 3.14 × 18

= 39.25

Radius, r = 39.25/2 × 3.14 = 6.25 cm

2) Semi vertical height, we would apply Pythagoras Theorem with the slant height of the cone being the hypotenuse, the radius being the adjacent side and the slant height being the opposite side.

h² = 18² - 6.25² = 284.9375

h = √284.9375 = 16.88 cm

3) Volume = 1/3πr²h where h represents the vertical height

Volume = 1/3 × 3.14 × 6.25² × 16.88 = 690.15 cm³