Question

Find the surface area of the cylinder. Show all work for credit. Leave your answers in terms of pi.
Radius: 5 m
Height: 9 m

Answer 1

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

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

We are given the radius \( r = 5 \) m and the height \( h = 9 \) m. Now we can substitute these values into the formula.

1. **Calculate the area of the two circular bases**:
\[
\text{Area of bases} = 2\pi r^2 = 2\pi (5)^2
\]
\[
= 2\pi (25) = 50\pi \, \text{m}^2
\]

2. **Calculate the area of the curved surface**:
\[
\text{Curved Surface Area} = 2\pi rh = 2\pi (5)(9)
\]
\[
= 2\pi (45) = 90\pi \, \text{m}^2
\]

3. **Combine the areas to find the total surface area**:
\[
\text{Total Surface Area} = \text{Area of bases} + \text{Curved Surface Area}
\]
\[
= 50\pi + 90\pi = 140\pi \, \text{m}^2
\]

Thus, the surface area of the cylinder is:

\[
\boxed{140\pi \, \text{m}^2}
\]