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Here is a tunnel for a toy train.
Work out the total area of
all six faces of the tunnel.
Give your answer in terms of t.
The diagram below shows the
cross section of the tunnel.
8 cm
с
2 cm
2 cm
10 cm
AD is a semicircular arc of radius 10 cm
BC is a semicircular arc of radius 8 cm
The length of the tunnel is 30 cm
Total marks: 5

Here Is A Tunnel For A Toy Train Work Out The Total Area Of All Six Faces Of The Tunnel Give Your Answer In Terms Of T The Diagram Below Shows The Cross Section class=

Sagot :

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The total area of all six faces of the tunnel is [tex]614.197\pi[/tex] square centimeters.

Procedure - Surface area of a tunnel for a toy train

The surface area of the solid ([tex]A[/tex]) 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:

[tex]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)[/tex]

[tex]A = 614.197\pi\,cm^{2}[/tex]

The total area of all six faces of the tunnel is [tex]614.197\pi[/tex] square centimeters. [tex]\blacksquare[/tex]

To learn more on surface areas, we kindly invite to check this verified question: https://brainly.com/question/2835293

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