To solve for the volume and the total surface area of the solid generated by rotating the rectangular strip around its 25 cm side, follow these steps:

1. Volume Calculation

When a rectangle is rotated about one of its sides, it forms a cylinder.

- Height of the Cylinder (h): 25 cm
- Radius of the Cylinder (r): 5 cm (the other side of the rectangle)

Volume of the Cylinder:
\[
\text{Volume} = \pi r^2 h
\]
\[
\text{Volume} = \pi \times (5)^2 \times 25
\]
\[
\text{Volume} = \pi \times 25 \times 25
\]
\[
\text{Volume} = 625 \pi
\]
\[
\text{Volume} \approx 625 \times 3.14 = 1962.5 \text{ cm}^3
\]

2. Total Surface Area Calculation

The total surface area of the cylinder consists of:
- The lateral surface area
- The area of the two circular bases

Lateral Surface Area:
\[
\text{Lateral Surface Area} = 2 \pi r h
\]
\[
\text{Lateral Surface Area} = 2 \pi \times 5 \times 25
\]
\[
\text{Lateral Surface Area} = 250 \pi
\]
\[
\text{Lateral Surface Area} \approx 250 \times 3.14 = 785 \text{ cm}^2
\]

Area of the Two Circular Bases:
\[
\text{Area of one base} = \pi r^2
\]
\[
\text{Area of one base} = \pi \times 25
\]
\[
\text{Area of one base} = 25 \pi
\]
\[
\text{Total area of two bases} = 2 \times 25 \pi = 50 \pi
\]
\[
\text{Total area of two bases} \approx 50 \times 3.14 = 157 \text{ cm}^2
\]

Total Surface Area:
\[
\text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of the two bases}
\]
\[
\text{Total Surface Area} = 785 + 157 = 942 \text{ cm}^2
\]

So, the correct option is:

A. 942.86 cm²