Question

A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi.

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
- \( \pi \) 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:

\(\text{Surface Area} \approx 24.76 \text{ cm}^2\)