Question

Prove that for a cone made by rolling up a semicircle, the area of the curved surface is twice the base area.​

Answer 1

Area of one square pyramid = Area of square + Area of four triangles. = (256 + .... Prove that for a cone made by bending a semicircle, the curved surface area is double the base area.

Answer 2

Answer:

Radius of the semicircle=R

Arc length=1/2×2πR=πR

Radius of the cone=r

Circumference of the cone=πr

2πr=πR

x=πR/2π=R/2

curved surface area of the cone=πrl=π×R/2×R{1/2πR²

Base area of the cone=πr²=π×(R/2)²

π×R²/4=1/4πR²

2×1/4πR²=1/2πR²

That means the curved surface area of the cone is twice it's base area.