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
- \( \pi \) is approximately 3.14
First, we need to find the radius \( r \) of the cylinder. The diameter is given as 1.5 cm, so the radius is half of the diameter:
\[ r = \frac{\text{Diameter}}{2} = \frac{1.5 \text{ cm}}{2} = 0.75 \text{ cm} \]
Now we can substitute the values into the surface area formula.
Given:
- \( r = 0.75 \text{ cm} \)
- \( h = 4.5 \text{ cm} \)
- \( \pi \approx 3.14 \)
Now substitute \( r \) and \( h \) into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 0.75 \times (4.5 + 0.75) \]
Calculating \( (4.5 + 0.75) \):
\[ 4.5 + 0.75 = 5.25 \]
Now substituting back into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 0.75 \times 5.25 \]
Calculating \( 2 \times 3.14 \times 0.75 \):
\[ 2 \times 3.14 = 6.28 \] \[ 6.28 \times 0.75 = 4.71 \]
Now calculating the final surface area:
\[ \text{Surface Area} = 4.71 \times 5.25 = 24.7575 \]
Thus, the surface area of the cylinder is approximately:
\[ \text{Surface Area} \approx 24.76 \text{ square centimeters} \]
Final answer:
\(\text{Surface Area} \approx 24.76 \text{ cm}^2\)