Answer:
125π√3/3 cm³ ≈ 226.72 cm³
Step-by-step explanation:
The length of the circular edge of the half-circle is ...
(1/2)C = (1/2)(2πr) = πr = 10π . . . . cm
This is the circumference of the circular edge of the cone, so the radius of the cone is found from ...
C = 2πr
10π = 2πr . . . . fill in the numbers; next, solve for r
r = 5 . . . . cm
The slant height of the cone is the original radius, 10 cm, so the height of the cone from base to apex is found from the Pythagorean theorem.
(10 cm)² = h² + r²
h = √((10 cm)² -(5 cm)²) = 5√3 cm
And the cone's volume is ...
V = 1/3·πr²h = (1/3)π(5 cm)²(5√3 cm)
V = 125π√3/3 cm³ ≈ 226.72 cm³
