Question

derive curved surface formula​

Answer 1

Answer:

In the cone below, hh is the height, LL is the slant height, cc is the circumference of the base, and rr is the radius of the base. How does it look when we unroll it?

If we unroll it, the shape is as follows:

It is a sector of a circle with radius LL and arc length cc. So the curved surface area of the cone is the area of the sector above. The area of a sector given the arc length cc and radius LL is given by A=\dfrac{1}{2}cLA=

2

1

cL. Now applying this to the cone, we have A=\frac{1}{2}cL,A=

2

1

cL, where LL is the slant height and cc is the circumference of the base. After some manipulations, A=\pi Lr,A=πLr, as given in the definition.