Question

What is the volume of earthwork (cubic metre) in embankment of 10 m long and 7m wide with the side slope of 2:1?

Answer 1

Given:

The dimensions of the embankment:

Length, L = 10 m

Width, B = 7 m

Side slope, S = 2:1

To find:

The volume of earthwork (in cubic meter)

Solution:

To find the volume of earthwork (in cubic meters) can be calculated by the following formula,

Area of the sides = $\frac{Sd^2}{2} + \frac{Sd^2}{2} = \frac{2Sd^2}{2} = Sd^2$

Area of centre = B * d

Volume = [Area of sides + Area of centre] * Length = [B*d + Sd²] * L

here

S = side slope

d = depth of the embankment

B = width

L = length

Now, we will substitute the given values in the formula of the volume, we get

The volume of earthwork is given by,

= [B*d + Sd²] * L

= [7*3 + 2*3²] * 10

= [21 + 2*9] * 10

= [21 + 18] * 10

= 39 * 10

= 390 m³

Thus, $\boxed{\bold{The\:volume\:of\:earthwork\:is\: 390\:m^3}}$.

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