Question

Find the length of the height of the cone. Diameter is 10cm and length of one side is 13cm

Answer 1

To find the height of the cone, we can use the relationship between the radius, height, and slant height of the cone. The slant height (l) forms a right triangle with the height (h) and the radius (r) of the base of the cone.

The given data is:
- Diameter of the cone = 10 cm, so the radius (r) = diameter / 2 = 10 cm / 2 = 5 cm
- Slant height (l) = 13 cm

Using the Pythagorean theorem:

\[
l^2 = r^2 + h^2
\]

Substituting the known values:

\[
13^2 = 5^2 + h^2
\]

Calculating \(13^2\) and \(5^2\):

\[
169 = 25 + h^2
\]

Now, rearranging the equation to solve for \(h^2\):

\[
h^2 = 169 - 25
\]

\[
h^2 = 144
\]

Taking the square root of both sides to find \(h\):

\[
h = \sqrt{144}
\]

\[
h = 12 \text{ cm}
\]

Thus, the height of the cone is **12 cm**.