Question

length 8.3 mm. Height 6.7 mm.
What is the surface area of this cylinder?
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

Answer 1

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

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

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

From your data, it seems you provided the height (6.7 mm) and potentially the diameter instead of the radius. We need to clarify the dimensions. If we assume that the length of 8.3 mm refers to the diameter, then we can find the radius \( r \) as follows:

\[
r = \frac{\text{diameter}}{2} = \frac{8.3 \, \text{mm}}{2} = 4.15 \, \text{mm}
\]

Now we have:
- Radius \( r = 4.15 \, \text{mm} \)
- Height \( h = 6.7 \, \text{mm} \)

Now we can substitute these values into the surface area formula:

\[
\text{Surface Area} = 2 \cdot \pi \cdot 4.15 \cdot (6.7 + 4.15)
\]

First, calculate \( h + r \):

\[
h + r = 6.7 + 4.15 = 10.85 \, \text{mm}
\]

Now substitute this into the surface area formula:

\[
\text{Surface Area} = 2 \cdot 3.14 \cdot 4.15 \cdot 10.85
\]

Calculating \( 2 \cdot 3.14 \):

\[
2 \cdot 3.14 = 6.28
\]

Now multiply this by \( 4.15 \):

\[
6.28 \cdot 4.15 \approx 26.073
\]

Now multiply by \( 10.85 \):

\[
26.073 \cdot 10.85 \approx 283.79405
\]

Now round to the nearest hundredth:

\[
\text{Surface Area} \approx 283.79 \, \text{mm}^2
\]

Thus, the surface area of the cylinder is approximately:

\[
\boxed{283.79 \, \text{mm}^2}
\]