Volume of a Solid: Two rectangular prisms with given dimensions for calculating volume.

To solve the problem of finding the volume of the solids shown in the image, we need to use the formula for the volume of a rectangular prism (also known as a cuboid). The formula is:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

Part (i):

The dimensions of the first solid are:
- Length = 12 cm
- Width = 3 cm
- Height = 10 cm

Using the formula for the volume of a rectangular prism:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

Substitute the given values:

\[
\text{Volume} = 12 \, \text{cm} \times 3 \, \text{cm} \times 10 \, \text{cm}
\]

First, multiply the length and width:

\[
12 \times 3 = 36
\]

Next, multiply the result by the height:

\[
36 \times 10 = 360
\]

So, the volume of the first solid is:

\[
\boxed{360} \, \text{cm}^3
\]

Part (ii):

The dimensions of the second solid are:
- Length = 10 cm
- Width = 5 cm
- Height = 25 cm

Using the same formula for the volume of a rectangular prism:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

Substitute the given values:

\[
\text{Volume} = 10 \, \text{cm} \times 5 \, \text{cm} \times 25 \, \text{cm}
\]

First, multiply the length and width:

\[
10 \times 5 = 50
\]

Next, multiply the result by the height:

\[
50 \times 25 = 1250
\]

So, the volume of the second solid is:

\[
\boxed{1250} \, \text{cm}^3
\]

Final Answers:

- Volume of the first solid: \(\boxed{360} \, \text{cm}^3\)
- Volume of the second solid: \(\boxed{1250} \, \text{cm}^3\)