Question

What is the total surface area of the cylinder from Part A? (Radius is 2.5 meters and height is 7 meters).

Answer 1

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

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

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

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

Now plug the values into the formula:

1. Calculate the lateral surface area:
\[
\text{Lateral Surface Area} = 2\pi rh = 2\pi(2.5)(7)
\]

2. Calculate the area of the two circular bases:
\[
\text{Area of Bases} = 2\pi r^2 = 2\pi(2.5^2)
\]

Now we can compute these:

1. Lateral Surface Area:
\[
2\pi(2.5)(7) = 35\pi \approx 35 \times 3.14 \approx 109.9 \, \text{m}^2
\]

2. Area of Bases:
\[
2\pi(2.5^2) = 2\pi(6.25) = 12.5\pi \approx 12.5 \times 3.14 \approx 39.25 \, \text{m}^2
\]

Now, add both areas to get the total surface area:
\[
\text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of Bases} = 35\pi + 12.5\pi = 47.5\pi
\]

Finally, calculating the numerical value:
\[
47.5\pi \approx 47.5 \times 3.14 \approx 149.07 \, \text{m}^2
\]

So, the total surface area of the cylinder is approximately \( 149.07 \, \text{m}^2 \).