Answer: 10.008 cm
Explanation:
The formula for the surface area of a cone is:
SA = πr² + πrℓ
where r is the radius of the base, ℓ is the slant height, and π is the mathematical constant pi.
In this case, we know that the radius of the cone is 5 cm and the surface area is 314 square centimeters. So we can write:
314 = π(5)² + π(5)ℓ
Simplifying the right-hand side:
314 = 25π + 5πℓ
Subtracting 25π from both sides:
314 - 25π = 5πℓ
Dividing both sides by 5π:
(314 - 25π) / (5π) = ℓ
Using a calculator to approximate π:
ℓ ≈ 10.008
So the slant height of the cone is approximately 10.008 cm.