一个长方体的正方形底面面积为 25 cm$^2$。阴影面的面积为 35 cm$^2$。 这个长方体的体积是多少？

1. Find the side length of the square base.

Let the side length of the square base be $s$.
$s^2 = 25$
$s = \sqrt{25} = 5\text{ cm}$

2. Find the height of the cuboid.

The shaded face is a rectangle with width $s$ and height $h$.
Area of shaded face $= s \times h = 35$
$5 \times h = 35$
$h = 35 \div 5 = 7\text{ cm}$

3. Calculate the volume of the cuboid.

Volume $= \text{Base Area} \times \text{Height}$
Volume $= 25 \times 7 = 175\text{ cm}^3$