Question

Use the image to answer the question.
13 cm
• - --
d = 10 cm
Find the length of the height of the cone.

Answer 1

To find the height of a cone given the radius and the slant height, you can use the Pythagorean theorem.

The formula is:
\[
l^2 = r^2 + h^2
\]
where:
- \( l \) is the slant height (13 cm)
- \( r \) is the radius (10 cm)
- \( h \) is the height we need to find

First, we identify the values:
- \( l = 13 \) cm
- \( r = 10 \) cm

Now, we can substitute these values into the formula:
\[
13^2 = 10^2 + h^2
\]

Calculating the squares:
\[
169 = 100 + h^2
\]

Next, subtract 100 from both sides:
\[
169 - 100 = h^2
\]
\[
69 = h^2
\]

Now, take the square root of both sides to find \( h \):
\[
h = \sqrt{69}
\]

Calculating \( \sqrt{69} \):
\[
h \approx 8.31 \text{ cm}
\]

So, the height of the cone is approximately **8.31 cm**.