Question

What is the total surface area of the cylinder from Part A? (Radius is 2.5 meters and height is 7 meters). Use 3.14 for pi. Show your work

Answer 1

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

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

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.

Given:
- Radius \( r = 2.5 \) meters
- Height \( h = 7 \) meters

Now plug in the values:

1. First calculate \( h + r \):
\[
h + r = 7 + 2.5 = 9.5 \text{ meters}
\]

2. Now calculate \( 2\pi r(h + r) \):
\[
\text{Total Surface Area} = 2 \times 3.14 \times 2.5 \times 9.5
\]

Calculating step by step:

- Calculate \( 2 \times 3.14 \):
\[
2 \times 3.14 = 6.28
\]

- Calculate \( 6.28 \times 2.5 \):
\[
6.28 \times 2.5 = 15.7
\]

- Now calculate \( 15.7 \times 9.5 \):
\[
15.7 \times 9.5 = 149.15
\]

Thus, the total surface area of the cylinder is:

\[
\text{Total Surface Area} \approx 149.15 \text{ square meters}
\]

Final answer:
\[
\text{Total Surface Area} \approx 149.15 \, \text{m}^2
\]