Question

What is the slant height of the cone? Height is 9ft and radius is 8ft

9.8ft; use the Pythagorean theorem
97ft; use the volume formula
12ft; use the Pythagorean theorem
7ft; use the volume formula

Answer 1

To find the slant height of a cone, we can use the Pythagorean theorem. The slant height (denoted as \( l \)), the height (denoted as \( h \)), and the radius (denoted as \( r \)) form a right triangle:

\[
l^2 = r^2 + h^2
\]

where:
- \( r = 8 \) ft (the radius),
- \( h = 9 \) ft (the height).

Now we can substitute the values into the equation:

\[
l^2 = 8^2 + 9^2
\]
\[
l^2 = 64 + 81
\]
\[
l^2 = 145
\]

Now, take the square root of both sides to find \( l \):

\[
l = \sqrt{145} \approx 12.04 \text{ ft}
\]

So the slant height of the cone is approximately 12 ft. Therefore, the correct answer is:

**12ft; use the Pythagorean theorem**.