Question

Here is a tunnel for a toy train.

Answer 1

The total area of all six faces of the tunnel is $614.197\pi$ square centimeters.

Procedure - Surface area of a tunnel for a toy train

The surface area of the solid ($A$) used to represent the tunnel for a toy train is the sum of its six faces (two semicircular sections, inner semicircular arc section, outer semicircular arc section, two rectangles).

Determination of the surface area of the tunnel based on information of the diagram

We calculate the surface area as following:

$A = 2\cdot \frac{\pi}{2} \cdot [(10\,cm)^{2}-(8\,cm)^{2}] + \pi\cdot (8\,cm)\cdot (30\,cm) + \pi\cdot (10\,cm)\cdot (30\,cm) + 2\cdot (2\,cm)\cdot (30\,cm)$

$A = 614.197\pi\,cm^{2}$

The total area of all six faces of the tunnel is $614.197\pi$ square centimeters. $\blacksquare$

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