WHat is the height of the right circular cone?

It has a 16 cm diameter, 15 cm height and 17 cm slant

1 answer

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.