Question

100 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!

Answer 1

Answer: The height of the cone is
`12 \text{ units}.`

Explanation:

We are given that
`L = \pi r √(r^2+h^2).` Plugging in the given values of
`L` and
`r` yields:

`65 \pi = 5 \pi √(25+h^2) \implies 13 = √(25+h^2).`

Now, squaring each side of the equation, and then isolating
`h^2` gives us
`h^2=144`, so
`\boxed{h=12}.` Note that
`h` cannot take any negative values because it is a side length.