Question

Find the surface area of the cylinder. Use the approximation of 3.14 for pi. An illustration shows a right circular cylinder with the axis labeled 15 and the radius of the bottom surface labeled 2. (1 point) Responses 204.1 204.1 565.2 565.2 408.2 408.2 1469.52

Answer 1

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

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

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

Given:
- Radius \( r = 2 \)
- Height \( h = 15 \)

Now, let's calculate the surface area step-by-step:

1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (2)^2 = 2 \times 3.14 \times 4 = 25.12
\]

2. Calculate the lateral surface area:
\[
2\pi rh = 2 \times 3.14 \times 2 \times 15 = 2 \times 3.14 \times 30 = 188.4
\]

3. Now, add both areas together to find the total surface area:
\[
\text{Surface Area} = 25.12 + 188.4 = 213.52
\]

Thus, the surface area of the cylinder is approximately 213.52. However, none of the provided responses correspond to this value. Let's recheck the calculations.

Since it appears there may be a discrepancy, if we follow the assumption that \( r \) and \( h \) have been provided accurately, the closest option based on our calculations would be:

- 204.1
- 204.1
- 565.2
- 565.2
- 408.2
- 408.2
- 1469.52

None match the calculated surface area exactly, but you can review the problem setup or confirm the measurements given for recalculations.

If we had a mistake in using the values or interpreted them wrongly, please clarify, and I can assist accordingly. If you are sure about the values provided, it looks like our calculations suggest a value of about **213.52**, which does not appear in the choices given.