A circle of radius 10 is divided into four congruent sectors. One of these sectors is used to form the curved surface of a cone. What is the volume of this cone?

V ≈ 63.4

Step-by-step explanation:

The arc length of the segment becomes the circumference of the cone's base. Therefore, we can find the radius of the cone:

s = C

(90/360) 2π (10) = 2π r

r = 2.5

The radius of the segment is the slant length of the cone. So we can use Pythagorean theorem to find the cone's height.

l² = r² + h²

10² = 2.5² + h²

h = √93.75

The volume of the cone is:

V = π/3 r² h

V = π/3 (2.5) ² √93.75

V ≈ 63.4