Question

During heavy rain, a section of a mountainside measuring 2.3 km horizontally (perpendicular to the slope), 0.75 km up along the slope, and 1.4 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.52 km x 0.52 km and that the mass of a cubic meter of mud is 1900 kg. What is the mass of the mud sitting above a 5.5 m2 area of the valley floor?

Answer 1

93328 kg

Step-by-step explanation:

`\rho` = Density of mud = 1900 kg/m³

Volume of the cuboid is given by

`V=2300* 750* 1.4\\\Rightarrow V=2415000\ m^3`

Volume is also given by

`V=Al\\\Rightarrow l=(V)/(A)\\\Rightarrow l=(2415000)/(520* 520)\\\Rightarrow l=8.9312\ m`

The length of the cuboid is 0.89312 m

For the small volume

`V_a=al\\\Rightarrow V_a=5.5* 8.9312\\\Rightarrow V_a=49.12\ m^3`

Mass is given by

`m=\rho V_a\\\Rightarrow m=1900* 49.12\\\Rightarrow m=93328\ kg`

The mass of the mud is 93328 kg