Surface area = lateral area + base area
Base area = r²π
Lateral area = πra (a is apotheme, 0,51 m)
0,51 m = cm 51 (0,51×100)
Find the radius. As you can see, the apotheme is the hypothenuse of the right triangle inside the cone. The heught of the cone is one leg. Apply Pitagora.
r = √51²-24² = √2601-576 = √2025 = 45 cm
Base area = 45²*pi = 2025pi cm²
Lateral area = 45*51*pi = 2295pi cm²
Surface area = 0,2025+0,2295 = 4320pi cm²