Question

What is the total surface area of a cylinder whose radius is 18 m and height is 16 m? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. ___ square meters

Answer 1

The total surface area \( A \) of a cylinder is given by the formula:

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

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

For the given cylinder:
- Radius \( r = 18 \) m
- Height \( h = 16 \) m

Substituting these values into the formula:

\[
A = 2 \times \pi \times 18 \times (16 + 18)
\]

Calculating \( 16 + 18 \):

\[
16 + 18 = 34
\]

Now, substitute back into the equation:

\[
A = 2 \times \pi \times 18 \times 34
\]

Now, calculate \( 2 \times 18 \):

\[
2 \times 18 = 36
\]

So we can now simplify our equation to:

\[
A = 36 \times \pi \times 34
\]

Calculating \( 36 \times 34 \):

\[
36 \times 34 = 1224
\]

Therefore we continue with:

\[
A = 1224 \times \pi
\]

Now, substituting \( \pi \approx 3.14 \):

\[
A \approx 1224 \times 3.14
\]

Now calculate:

\[
1224 \times 3.14 = 3845.76
\]

Thus, the total surface area of the cylinder is approximately:

\[
\boxed{3845.76} \text{ square meters}
\]