The surface area of a cylinder can be calculated using the formula:
[tex]\[ \text{Surface Area} = 2 \pi r (r + h) \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base of the cylinder
- [tex]\( h \)[/tex] is the height of the cylinder
- [tex]\( \pi \)[/tex] (Pi) is a constant approximately equal to 3.141592653589793
Given:
- Radius [tex]\( r = 2 \)[/tex] units
- Height [tex]\( h = 22 \)[/tex] units
Let's plug these values into the formula to find the surface area:
1. First, we need to calculate the term inside the parentheses [tex]\((r + h)\)[/tex]:
[tex]\[ r + h = 2 + 22 = 24 \][/tex]
2. Then, we use the surface area formula:
[tex]\[ \text{Surface Area} = 2 \pi r (r + h) \][/tex]
Substituting the given values:
[tex]\[ \text{Surface Area} = 2 \pi \times 2 \times 24 \][/tex]
3. Simplify the expression:
[tex]\[ \text{Surface Area} = 2 \times 2 \times 24 \times \pi \][/tex]
[tex]\[ \text{Surface Area} = 4 \times 24 \times \pi \][/tex]
[tex]\[ \text{Surface Area} = 96 \times \pi \][/tex]
4. Finally, multiply by [tex]\(\pi\)[/tex]:
[tex]\[ \text{Surface Area} = 96 \times 3.141592653589793 \][/tex]
Therefore, the surface area of the cylinder is approximately 301.59289474462014 square units.
