Question

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

Answer 1

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

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

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

Given:
- Length (diameter) = 8.3 mm
- Height = 6.7 mm

First, we need to find the radius:
\[
r = \frac{\text{diameter}}{2} = \frac{8.3 \, \text{mm}}{2} = 4.15 \, \text{mm}
\]

Now we substitute the values into the surface area formula.

First, calculate \( 2\pi r^2 \):
\[
2\pi r^2 = 2 \cdot 3.14 \cdot (4.15)^2
\]

Calculating \( (4.15)^2 \):
\[
(4.15)^2 = 17.2225
\]
Now substituting this back into our formula:
\[
2\pi r^2 = 2 \cdot 3.14 \cdot 17.2225 \approx 108.0893 \, \text{mm}^2
\]

Next, we calculate \( 2\pi rh \):
\[
2\pi rh = 2 \cdot 3.14 \cdot 4.15 \cdot 6.7
\]
Calculating \( 4.15 \cdot 6.7 \):
\[
4.15 \cdot 6.7 = 27.855
\]
Now substituting this back into our formula:
\[
2\pi rh = 2 \cdot 3.14 \cdot 27.855 \approx 175.6881 \, \text{mm}^2
\]

Now we can find the total surface area by adding both parts together:
\[
\text{Surface Area} \approx 108.0893 + 175.6881 \approx 283.7774 \, \text{mm}^2
\]

Finally, rounding to the nearest hundredth:
\[
\text{Surface Area} \approx 283.78 \, \text{mm}^2
\]

Thus, the surface area of the cylinder is approximately **283.78 mm²**.