Question

Prove that for a cone made by bending a semicircle, the curved surface area is double the base area.

Answer 1

Let the radius of the bigger circle be R units.

Slant height of the cone = Radius of the bigger circle = R units

Since the cone is made from a semi-circular sector, the central angle = = 180°.

∴ Radius of the small circle = of the radius of the larger circle

∴ Base-radius of the cone

Curved surface area of the cone = πrl

Therefore, curved surface area of the cone is double the base area.