Question

the diameter is 16
the lenght is 7
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 can use the formula:

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

where \( r \) is the radius and \( h \) is the height of the cylinder.

Given:
- Diameter = 16
- Length (height) = 7

First, we calculate the radius:

\[
r = \frac{\text{Diameter}}{2} = \frac{16}{2} = 8
\]

Now, substitute the values of \( r \) and \( h \) into the surface area formula:

\[
\text{Surface Area} = 2 \times \pi \times 8 \times (7 + 8)
\]

Calculating \( h + r \):

\[
h + r = 7 + 8 = 15
\]

Now, substitute into the surface area formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 8 \times 15
\]

Calculating \( 2 \times 3.14 \):

\[
2 \times 3.14 = 6.28
\]

Now, calculate:

\[
6.28 \times 8 = 50.24
\]

Next, multiply by 15:

\[
50.24 \times 15 = 753.6
\]

Thus, the surface area of the cylinder is approximately:

\[
\text{Surface Area} \approx 753.6
\]

Finally, rounding to the nearest hundredth, the surface area is:

\[
\text{Surface Area} \approx 753.60
\]

So, the final answer is:

\[
\text{Surface Area} = 753.60
\]