如下图所示，将六个相同的立方体粘在一起形成一个长方体。每个立方体的边长为 1 cm。然后将该长方体完全浸入一桶红漆中。求该长方体被染成红色的总面积。 答: ___ $\text{cm}^2$

1. Determine the dimensions of the cuboid

The cuboid is made of 6 cubes in a 3 by 2 by 1 arrangement.
Length $= 3 \text{ cm}$
Width $= 2 \text{ cm}$
Height $= 1 \text{ cm}$

2. Calculate the total surface area of the cuboid

$\text{Total surface area} = 2(lw + lh + wh)$
$= 2(3 \times 2 + 3 \times 1 + 2 \times 1)$
$= 2(6 + 3 + 2)$
$= 2(11)$
$= 22 \text{ cm}^2$