A sector of angle 120∘ is removed from a thin circular sheet of radius 30 cm. 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 line, and the volume of the cone?
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The base radius is 20 cm
The semi-vertical line is 22.36 cm
The volume of the cone is 9366.13 cm³
Step-by-step explanation:
Slant height = Original radius
∴ Slant height = l = 30 cm
From question, 120° sector is removed, thus, the remaining sector is 240°.
Base radius = (240°/360°) × 2π × 30
∴ Base radius = r = 20 cm
The semi-vertical line is obtained by applying Pythagoras theorem,
h = √(30² + 20²)
∴ Semi-vertical line = h = 22.36 cm
The volume of cone is given by the formula:
V = πr²h/3
On substituting the values, we get,
V = π × (20)² × 22.36/3
∴ Volume of cone = 9366.13 cm³
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