# Civil Engineering and Construction Pathways : Length of an Arc and Volume of Dirt

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A.

The diagram over shows an area of a railway cutting that has failed in the form of a shallow rotational slip. Using radians as a measure of angular displacement determine the length of the failure surface AB.

b.

A partially completed site survey of a quadrilateral site is given below.

You are responsible for ordering a perimeter security fence. What is the minimum number of panels you would order if the length of each panel was 2.6 m?

Assuming the site is flat and that 17% of the site is contaminated by heavy metals, determine the number of trips that will be required to a license landfill the contaminated ground is to be excavated to a depth of 3.2 m. It may be assumed that one muck-away truck can transport 15 m3 of in-situ contaminated soil.

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The length of an arc and volume of dirt are calculated and discussed in the solution. The solution is detailed and well presented.

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Problem 1:

The diagram below shows an area of a railway cutting that has failed in the form of a shallow rotational slip. Using radians as a measure of angular displacement determine the length of the failure surface AB.

Solution:

If we have the radius and the opening angle, we can compute the length of the arc AB as well as the length of chord AB.

The arc AB

From the definition of the radian, we can write:

where α = the angle taken in radians:

As a result, the length of the arc ...

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