Answer:
Step-by-step explanation:
You want the slant height and surface area of a cone with base radius 2 cm and height 2√3 cm.
Slant height
The Pythagorean theorem tells you the slant height is ...
ℓ² = b² +h²
ℓ² = (2 cm)² +(2√3 cm)² = (4 +12) cm² = 16 cm²
ℓ = √(16 cm²) = 4 cm
Area
The base area is ...
A = πr²
The lateral area is ...
A = πrℓ
So, the total area is ...
SA = πr² +πrℓ = πr(r +ℓ)
SA = π(2 cm)(2 +4 cm) = 12π cm²
The surface area of the cone is 12π square centimeters.
__
Additional comment
We have used the symbol ℓ for the slant height, more or less matching the symbol in the problem statement. The sans-serif lower-case L is problematic, often being confused with the upper-case I (eye), and/or a vertical bar (|). This attempt at a script lower-case L is the best we can do with available fonts.
