Assuming that the units are in cm
Given,
Diameter of the cone = 12 cm
Using the above, the radius of the cone can be determined, which is half the diameter of the cone
∴ Radius of the cone (r) = 12/2 = 6 cm
Height of the cone (h) = 7 cm
Using the above, slant height (s) = √(r² + h²) = √(6² + 7²) = √36 + 49 = √85 = 9.22 cm
π = 3.14
Now using the above values, we can calculate the total surface area of the cone.
Total surface area of the cone (A) = Lateral surface area of the cone (L) + Base surface area of the cone (B)
Lateral surface area of the cone (L) = π r s = 3.14 x 6 x 9.22 = 173.70 cm²
Base surface area of the cone (B) = π r² = 3.14 x 6² = 113.04 cm²
Total surface area of the cone = L + B = 173.70 + 113.04 = 286.74 cm²
