Question

Could you please help me figure out what the slant height is? Radius=5
Height=11
Slant=?

Answer 1

12.08

Explanation:

Using Pythagoras Theorem

`s {}^(2) = r {}^(2) + h {}^(2)`

`s {}^(2) = 5 {}^(2) + 11 {}^(2)`

`s {}^(2) = 121 + 25 = 146`

`s = √(146)`

`s = 12.08`

Answer 2

s =
`\sqrt{146`

Explanation:

We can create a triangle cross-section with the given radius and height as its dimensions. Because this is a cone, we know that the radius and height are at a right angle to each other. Thus, this cross-section is a right triangle, and we can apply the Pythagorean Theorem to solve for the slant height.

r² + h² = s²

↓ plugging in the given values

5² + 11² = s²

↓ simplifying the exponents

25 + 121 = s²

↓ simplifying the addition

146 = s²

↓ square-rooting both sides

s =
`\bold{√(146)}`