Question

What is the surface area of this cylinder?
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. r=2mmt h=1mm

Answer 1

The surface area \( A \) of a cylinder can be calculated using the formula:

\[
A = 2\pi r(h + r)
\]

Where:
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder

Given:
- \( r = 2 \, \text{mm} \)
- \( h = 1 \, \text{mm} \)

Let's substitute the values into the formula.

1. Calculate \( h + r \):
\[
h + r = 1 \, \text{mm} + 2 \, \text{mm} = 3 \, \text{mm}
\]

2. Now, substitute \( r \) and \( h + r \) into the surface area formula:
\[
A = 2 \times 3.14 \times 2 \, \text{mm} \times 3 \, \text{mm}
\]

3. Calculate the surface area:
\[
A = 2 \times 3.14 \times 2 \times 3 = 2 \times 3.14 \times 6
\]
\[
A = 2 \times 18.84 = 37.68 \, \text{mm}^2
\]

Thus, the surface area of the cylinder is approximately \( 37.68 \, \text{mm}^2 \) when rounded to the nearest hundredth.