Answer:
A = 326,73 cm²
Step-by-step explanation:
The area of a circular cone is area of the base (A₁ ) plus area lateral ( area of a circular sector of radius the slant height )
Then we proceed to calculate the area of the base A₁
diameter of circular base is 8 cm then the radius is 4 cm and the area is:
A₁ = π*r²  =  3,14* (4)²
A₁ = 3,1416*16   =  50,2656 cm²
Now Lateral area of the cone (A₂) is equal to the area of a circular sector with radius the slant height. We will calculate it, taken into account that this circular sector is part of a circle of radius the slant height.
Between the area of circular sector with radius the slant height and the area of the circle with the same radius there is a linear relation. That is we can calculate area of a circular sector by rule of three as follows:
The length of the circular sector is the length of the circle of the base of the cone, that is:
L = 2*π*(4)
L = 2*3,1416*4
L = 25,1328 cm
Then we have a circular sector of length 25,1328 cm 
The area of the circle of radius 22 cm is:
A(c)  = π*(22)²     ⇒   A(c)  = 1520,5344 cm²
And the length of this circle is:
L(c)  =  2*π*(22)     ⇒   138,2304 cm
Then we apply a rule of three
For a length of      138,2304 cm  ⇒⇒⇒  (area)  1520,5344 cm²
Then for a length of  25,1328 cm   ⇒⇒⇒(area)   A₂ (??) 
Therefore:
A₂ =  (25,1328)*1520,5344)/ 138,2304
A₂ = 276,4608 cm²
Then total area of the cone is:
A = A₁  +  A₂
A =  50,2656  +276,4608
A  = 326,7264 cm²
Round answer  A = 326,73 cm²