To find the height of the right circular cone, we can use the relationship between the diameter, height, and slant height of the cone.
In a right circular cone, the height (\(h\)), radius (\(r\)), and slant height (\(l\)) are related by the Pythagorean theorem:
\[ l^2 = r^2 + h^2 \]
From the problem, we know:
- The diameter of the cone is 16 cm, so the radius \(r\) is half of the diameter: \[ r = \frac{16}{2} = 8 \text{ cm} \]
- The slant height \(l\) is given as 17 cm.
Now we can plug in the values into the Pythagorean theorem:
\[ 17^2 = 8^2 + h^2 \]
Calculating the squares:
\[ 289 = 64 + h^2 \]
Now, we can isolate \(h^2\):
\[ h^2 = 289 - 64 \] \[ h^2 = 225 \]
Taking the square root of both sides gives:
\[ h = \sqrt{225} = 15 \text{ cm} \]
Thus, the height of the right circular cone is 15 cm.
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