Answer:
162.8 cm²
Explanation:
The curved surface area of a cone can be calculated using the formula:
Curved Surface Area = πrℓ
where r is the base radius of the cone and ℓ is the slant height of the cone.
To find the slant height, we can use the Pythagorean theorem:
ℓ² = r² + h²
where h is the height of the cone.
We know that the height of the cone is not given in the problem statement. However, we can use the length of the cone to find the height. The length of the cone is the distance from the apex of the cone to the edge of the base. This is also the hypotenuse of a right triangle with height h and base radius r. So we can use the Pythagorean theorem again:
8² = r² + h²
h² = 8² - r²
h = √(8² - 5²) = √(64 - 25) = √39
Therefore, the slant height of the cone is ℓ = √(r² + h²) = √(5² + 39) = √(164) = 2√41.
Now we can use the formula for the curved surface area:
Curved Surface Area = πrℓ = π(5)(2√41) = 10π√41 ≈ 162.8 cm²
Therefore, the curved surface area of the cone is approximately 162.8 cm²