Question

The surface area of this cone is 314 square centimeters. What is the slant height of this

cone?
Use pi ≈ 3.14 and round your answer to the nearest hundredth.
radius= 5 cm

Answer 1

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.