Answer:
V ≈ 63.4
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