The surface area of a given cone is 1,885.7143 square inches. What is the slang height?

If , the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

Where:

- Base radius of the cone, measured in inches.

- Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

Where is the altitude of the cone, measured in inches. If , then:

And:

Given that , the following second-order polynomial is obtained:

Roots can be found by the Quadratic Formula:

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

answer:

step-by-step explanation: