Question

Find the surface area of the cone. Leave answer in terms of pi.
Radius: 5 cm
height: 12 cm

Answer 1

To find the surface area of a cone, we use the formula:

\[
\text{Surface Area} = \pi r (r + l)
\]

where \( r \) is the radius, and \( l \) is the slant height of the cone. The slant height can be calculated using the Pythagorean theorem:

\[
l = \sqrt{r^2 + h^2}
\]

Given:
- Radius \( r = 5 \, \text{cm} \)
- Height \( h = 12 \, \text{cm} \)

First, we calculate the slant height \( l \):

\[
l = \sqrt{r^2 + h^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, \text{cm}
\]

Now, we can substitute \( r \) and \( l \) into the surface area formula:

\[
\text{Surface Area} = \pi r (r + l) = \pi \times 5 \times (5 + 13)
\]

Calculate \( 5 + 13 \):

\[
5 + 13 = 18
\]

So, the surface area becomes:

\[
\text{Surface Area} = \pi \times 5 \times 18 = 90\pi \, \text{cm}^2
\]

Thus, the surface area of the cone is:

\[
\boxed{90\pi \, \text{cm}^2}
\]