Question

Find the surface area of a cylinder with a base radius lenght of 5 ft. and a height of 8 ft. Use pi = 3.14

Answer 1

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

\[
\text{Surface Area} = 2\pi r(h + r)
\]

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

In your case, the radius \( r \) is 5 ft and the height \( h \) is 8 ft. Let's plug in these values:

1. Calculate the lateral surface area (side surface area):
\[
\text{Lateral Surface Area} = 2\pi rh = 2 \times 3.14 \times 5 \times 8
\]

\[
= 2 \times 3.14 \times 40
\]

\[
= 2 \times 125.6 = 251.2 \text{ ft}^2
\]

2. Calculate the area of the two circular bases:
\[
\text{Area of Bases} = 2\pi r^2 = 2 \times 3.14 \times 5^2
\]

\[
= 2 \times 3.14 \times 25
\]

\[
= 2 \times 78.5 = 157 \text{ ft}^2
\]

3. Now, add both areas to get the total surface area:
\[
\text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of Bases} = 251.2 + 157
\]

\[
= 408.2 \text{ ft}^2
\]

Thus, the surface area of the cylinder is \( \boxed{408.2} \text{ ft}^2 \).