91Ó°ÊÓ

Dimensions of section of mountainside are $2.5\text{km}×0.80\text{km}×2.0\text{m}$

The dimensions of surface area of valley $0.40\text{km}×0.40\text{km}$

Density of mud ${\text{ÒÏ=1900°ì²µ/³¾}}^3$

The horizontal distance is A = 2.5 km = 2500 m , the height is,B = 0.80 km = 800m and the depth is, C = 2.0 m

Area of the valley floor is

The density of a material is given by mass per unit volume.A volume is the amount of space occupied by an object in three-dimensional space.

The expression for density is given as:
$\mathrm{ÒÏ}=\frac{m}{V}$… (i)

Here, $\mathrm{ÒÏ}$is the density, $m$is the mass and$V$ is the volume

The volume of the section is calculated as:

Thus, the volume of the section is$4×{10}^6{\text{m}}^3$

Let d be the thickness of the mud after it has uniformly distributed in the valley.

So, the volume of the mud is,

$V=400\text{m}×400\text{m}×d$

Since the mud is distributed uniformly, therefore,

$$\begin{gathered} 400\text{m}×400\text{m}×d=4×{10}^6{\text{m}}^3 \\ d=25\text{m} \end{gathered}$$

Calculate the volume of mud over area of$\text{4.0}{\text{m}}^2$

$$\begin{gathered} V_{\text{m}}=4.0{\text{m}}^{\text{2}}×d \\ =4.0m^2×25\text{m} \\ =100.0{\text{m}}^{\text{3}} \end{gathered}$$

As each cubic meter corresponds to a mass of 1900 kg, the mass of that part of the mud can be calculated using the formula for the density.

Thus, the mass of that part of mud is$1.9×{10}^5\text{kg}$