Question

WHat is the height of the right circular cone?
It has a 16 cm diameter, 15 cm height and 17 cm slant

Answer 1

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**.