Answer:
V = 3π√7 cm³ ≈ 24.94 cm³
Explanation:
The radius of the finished cone can be found from the circumference of the finished cone, which is 3/4 of the circumference of the original paper circle.
Ccone = (3/4)Ccircle = (3/4)(2π(4 cm)) = 6π cm
This is related to the cone radius (x) by ...
Ccone = 2πx = 6π cm
x = 3 cm . . . . . . . . . 3/4 of the circle's radius
The height of the cone is given by the Pythagorean theorem:
(4 cm)² = h² + x²
h² = (4 cm)² -(3 cm)² = (16 -9) cm²
h = √7 cm
Now, we can use the formula for the volume of a cone:
V = (1/3)πr²h
= (1/3)π(3 cm)²(√7 cm)
V = 3π√7 cm³ ≈ 24.94 cm³