Question

Find the surface area of the cylinder.
Imagine a small line on top of the cylinder labelled "4m"
The side of the cylinder is labelled "10m"

Answer 1

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

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

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

From your description:
- The height \( h \) of the cylinder is \( 10 \, \text{m} \).
- The diameter of the cylinder seems to be indicated by the "4m" line on the top of the cylinder, implying the diameter is \( 4 \, \text{m} \). Therefore, the radius \( r \) is half of the diameter:

\[
r = \frac{4 \, \text{m}}{2} = 2 \, \text{m}
\]

Now, substituting \( r \) and \( h \) into the surface area formula:

\[
\text{Surface Area} = 2\pi (2 \, \text{m})(10 \, \text{m} + 2 \, \text{m})
\]
\[
= 2\pi (2)(12)
\]
\[
= 48\pi \, \text{m}^2
\]

Finally, if you want a numerical approximation using \( \pi \approx 3.14 \):

\[
\text{Surface Area} \approx 48 \times 3.14 \approx 150.72 \, \text{m}^2
\]

Thus, the surface area of the cylinder is approximately \( 150.72 \, \text{m}^2 \) or exactly \( 48\pi \, \text{m}^2 \).