Surface Area

lateral area of cone   =   pi * slant height * radius of the base

 

The radius of the base is  3  inches.

It looks like  6 inches  is the slant height.

 

lateral area of cone   =   pi * 6 * 3   in²

lateral area of cone  =   18pi   in²

 

lateral area of cylinder   =   circumference of base * height

lateral area of cylinder   =   2pi * radius of base * height

 

The radius of the base is  3 inches.

The height is  5 inches.

 

lateral area of cylinder   =   2pi * 3 * 5  in²

lateral area of cylinder   =   30pi  in²

 

area of base   =   pi * radius²

area of base   =   pi * 3²   in²

area of base   =   9pi  in²

 

total surface area   =   lateral area of cone + lateral area of cylinder + area of base

total surface area   =   18pi  in²   +   30pi  in²   +   9pi  in²

total surface area   =   57pi  in²

total surface area   ≈   57(3.14)  in²

total surface area   ≈   178.98  in²