Question

Look at the cone below.

9 ft and 41 ft

How many feet long is the radius of the cone?

Answer 1

To find the radius of the cone, we need to know which measurement corresponds to the height and which corresponds to the slant height or the diameter.

In your statement, it appears you mentioned two dimensions: 9 ft and 41 ft.

Assuming:
- The height of the cone is 9 ft.
- The slant height of the cone is 41 ft.

We can use the Pythagorean theorem to find the radius (r) of the cone. The relationship between the height (h), the radius (r), and the slant height (l) is given by:

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

Substituting the known values:

\[
41^2 = r^2 + 9^2
\]

This simplifies to:

\[
1681 = r^2 + 81
\]

Now, we subtract 81 from both sides:

\[
1681 - 81 = r^2
\]
\[
1600 = r^2
\]

Now, take the square root of both sides to find the radius:

\[
r = \sqrt{1600} = 40 \text{ ft}
\]

So, the radius of the cone is **40 feet**.