Question
Look at the cone below.
5 ft5\ \text{ft}5 ft
13 ft13\ \text{ft}13 ft
How many feet long is the radius of the cone?
5 ft5\ \text{ft}5 ft
13 ft13\ \text{ft}13 ft
Answers
GPT-4o mini
To find the radius of the cone, we need to gather more information about the cone's dimensions. The dimensions provided (5 ft and 13 ft) are likely the height and the slant height or the diameter of the base.
If we assume the 5 ft is the height of the cone and the 13 ft is the slant height, we can use the Pythagorean theorem to find the radius. The formula is:
\[
r = \sqrt{(l^2 - h^2)}
\]
where \( r \) is the radius, \( l \) is the slant height, and \( h \) is the height.
Using the provided values:
- \( l = 13 \, \text{ft} \)
- \( h = 5 \, \text{ft} \)
Plugging in these values:
\[
r = \sqrt{(13^2 - 5^2)} = \sqrt{(169 - 25)} = \sqrt{144} = 12 \, \text{ft}
\]
Thus, the radius of the cone is 12 feet.
If we assume the 5 ft is the height of the cone and the 13 ft is the slant height, we can use the Pythagorean theorem to find the radius. The formula is:
\[
r = \sqrt{(l^2 - h^2)}
\]
where \( r \) is the radius, \( l \) is the slant height, and \( h \) is the height.
Using the provided values:
- \( l = 13 \, \text{ft} \)
- \( h = 5 \, \text{ft} \)
Plugging in these values:
\[
r = \sqrt{(13^2 - 5^2)} = \sqrt{(169 - 25)} = \sqrt{144} = 12 \, \text{ft}
\]
Thus, the radius of the cone is 12 feet.