Trigonometry

Question

A paper come is unfolded to reveal that it is formed using a sector of a circle with radius 3 inches. If the arc length around the top of the cone is 7.7 inches what is the surface area of the outside of the cone? Round to the nearest tenth. 

Answer 1

As the cone is made up by foling a sector of a circle,then again unfolded to get the initial sector .So radius of the cirlce will be treated as  slanted length of the cone l=3 inches,

and length of the arc will form the perimeter of the base =2*pi*r=7.7 inches

                            ==> pi*r= 7.7/2 = 3.85 inches

 

Surface area of the cone = pi*r*l =(pi*r)*l

                                                  =3.85*3

                                                  = 11.55 square inches