What is the exact surface area of this right cone a.1944 pi cm sq b.5346 pi cm sq c.1701 pi cm sq d. 1215 pi cm sq

The correct answer is:  [A]:  " 1944 pi cm sq" . 

The exact surface area of the given "right cylinder" is:  " 1,944 π  cm² " .


Explanation:

The formula for the "surface area, S.A." of a right cone is:

       →   S. A.  = π r [ r + √(h² + r²) ]

    in which:   "S. A." is the "surface area" (in units of "cm² " ; in our case) ;
                                  →  for which we shall solve; 

                        π = π ; (Note, we are asked to solve for the EXACT surface area of the given "right cone" ; so we shall solve in terms of "π" ; & we note that the answer choices provided are all "in terms of π" ; 

                     " r = "radius" of the [circular base] = diameter / 2 ;

                          = 54 cm / 2 = 27 cm ; 

                     " h = perpendicular height = 36 cm " ;
 

→  Plug in our known values into the formula/equation ;
         for the "surface area, S.A." of a right cone  to solve:


       →   S. A.  =  π r [ r + √(h² + r²) ]  ;

       →   S.A.   =  π * (27 cm) * [ 27 cm + √[ (36 cm)² + (27 cm)² ]  ;

                       =  π * (27 cm) * [ 27 cm + √[ (36² * cm²) + (27² cm²) ]  ;
                       
                       =  π * (27 cm) * [ 27 cm + √[ (1296 cm²)  + (729 cm²) ]  ;

                       =  π * (27 cm) * [ 27 cm + √ [ (1296 + 729) cm² ]  ;

                       =  π * (27 cm) * [ 27 cm + √ [ (1296 + 729) cm² ]  ;

                       =  π * (27 cm) * [ 27 cm + √ [ (1296 + 729) cm² ]  ;

                       =  π * (27 cm) * [ 27 cm + √ (2025 cm² ]  ;

                       =  π * (27 cm) * [ 27 cm + √ (2025 cm² ]  ;

                       =  π * (27 cm) * [ 27 cm + 45 cm ]  ;

                       =  π * (27 cm) * [ 27 cm + 45 cm ]  ;

                       =  π * (27 cm) * [ 72 cm ]  ;

                       =  π * (27 cm) * [ 72 cm ]  ;
 
                       =  (27 * 72) * π  cm²  ; 

                       =  (27 * 72) * π  cm²  ; 

                          =   " 1,944 π  cm² " .

 [A]:  " 1944 pi cm sq" . 

The exact surface area of the given "right cylinder" is:  " 1,944 π  cm² " .