200 Followers Question by Dr. Warm

The surface area of the outer surface is $(3^2-1^2)(6)=(8)(6)=48~cm^2$ .

The surface area of the inner surface is $(1^2)(4)(6)=24~cm^2$ .

The total surface area of the structure is $48+24=72~cm^2$

$\large\color{#69047E}\text{answer:}$ $\large\boxed{\color{#D61F06}72~cm^2}$

As depicted in the question, the total surface area of the structure will consist of the external light blue surface areas plus the internal dark blue tunnel areas.

The total external light blue surface area = $6\times (3\times 3 - 1) = 48$ .

The total internal dark blue tunnel areas = $6\times 4 = 24$ .

Thus, the total surface area = $48 + 24 = \boxed{72}$