Question
Look at the cone below.
16 ft16\ \text{ft}16 ft
65 ft65\ \text{ft}65 ft
How many feet long is the radius of the cone?
Answers
GPT-4o mini
To find the radius of the cone, we can use the properties of a right triangle formed by the radius, height, and slant height of the cone.
In this case, the height (h) of the cone is 16 ft, and the slant height (l) is 65 ft. The radius (r) is what we need to find.
Using the Pythagorean theorem, we have:
\[
l^2 = r^2 + h^2
\]
Substituting the given values into the equation:
\[
65^2 = r^2 + 16^2
\]
\[
4225 = r^2 + 256
\]
Now we can isolate \( r^2 \):
\[
r^2 = 4225 - 256
\]
\[
r^2 = 3969
\]
Taking the square root of both sides gives us:
\[
r = \sqrt{3969}
\]
\[
r = 63 \text{ ft}
\]
So, the radius of the cone is **63 feet**.
In this case, the height (h) of the cone is 16 ft, and the slant height (l) is 65 ft. The radius (r) is what we need to find.
Using the Pythagorean theorem, we have:
\[
l^2 = r^2 + h^2
\]
Substituting the given values into the equation:
\[
65^2 = r^2 + 16^2
\]
\[
4225 = r^2 + 256
\]
Now we can isolate \( r^2 \):
\[
r^2 = 4225 - 256
\]
\[
r^2 = 3969
\]
Taking the square root of both sides gives us:
\[
r = \sqrt{3969}
\]
\[
r = 63 \text{ ft}
\]
So, the radius of the cone is **63 feet**.