Question
Look at the cone below.
15 ft15\ \text{ft}15 ft
lll
8 ft8\ \text{ft}8 ft
How many feet long is the slant height of the cone? Click Here for Help Video.
Answers
GPT-4o mini
To find the slant height (l) of a cone, we can use the Pythagorean theorem. The slant height forms a right triangle with the height (h) and the radius (r) of the base of the cone.
Given:
- Height (h) of the cone = 8 ft
- Radius (r) of the base = 15 ft
The formula to find the slant height is:
\[
l = \sqrt{r^2 + h^2}
\]
Substituting the values:
\[
l = \sqrt{15^2 + 8^2}
\]
\[
l = \sqrt{225 + 64}
\]
\[
l = \sqrt{289}
\]
\[
l = 17 \text{ ft}
\]
Therefore, the slant height of the cone is **17 feet**.
Given:
- Height (h) of the cone = 8 ft
- Radius (r) of the base = 15 ft
The formula to find the slant height is:
\[
l = \sqrt{r^2 + h^2}
\]
Substituting the values:
\[
l = \sqrt{15^2 + 8^2}
\]
\[
l = \sqrt{225 + 64}
\]
\[
l = \sqrt{289}
\]
\[
l = 17 \text{ ft}
\]
Therefore, the slant height of the cone is **17 feet**.