Question
Look at the cone below.
28 ft28\ \text{ft}28 ft
53 ft53\ \text{ft}53 ft
How many feet long is the radius of the cone? Click Here for Help Video.
Answers
GPT-4o mini
To find the radius of the cone, we can use the formula for the dimensions of a right circular cone. The measurements typically consist of the height (h) and the slant height (l), with the radius (r) being the unknown.
Given that:
- Height (h) = 28 ft
- Slant height (l) = 53 ft
We can use the Pythagorean theorem, which states that in a right triangle:
\[ l^2 = r^2 + h^2 \]
We can rearrange this formula to solve for the radius (r):
\[ r^2 = l^2 - h^2 \]
\[ r = \sqrt{l^2 - h^2} \]
Now, we can substitute the known values:
1. Calculate \( l^2 \):
\[ l^2 = 53^2 = 2809 \]
2. Calculate \( h^2 \):
\[ h^2 = 28^2 = 784 \]
3. Now substitution gives:
\[ r^2 = 2809 - 784 = 2025 \]
4. Finally, taking the square root gives:
\[ r = \sqrt{2025} = 45 \]
Therefore, the radius of the cone is **45 ft** long.
Given that:
- Height (h) = 28 ft
- Slant height (l) = 53 ft
We can use the Pythagorean theorem, which states that in a right triangle:
\[ l^2 = r^2 + h^2 \]
We can rearrange this formula to solve for the radius (r):
\[ r^2 = l^2 - h^2 \]
\[ r = \sqrt{l^2 - h^2} \]
Now, we can substitute the known values:
1. Calculate \( l^2 \):
\[ l^2 = 53^2 = 2809 \]
2. Calculate \( h^2 \):
\[ h^2 = 28^2 = 784 \]
3. Now substitution gives:
\[ r^2 = 2809 - 784 = 2025 \]
4. Finally, taking the square root gives:
\[ r = \sqrt{2025} = 45 \]
Therefore, the radius of the cone is **45 ft** long.