Rectangular 67604

The Horniakovs dug a pit for a cesspool in the shape of a cuboid with bottom dimensions of 40*40 dm and a depth of 350 cm.
A) How many cubic meters of soil did they dig up?
B) The excavated soil was evenly spread and pressed onto a rectangular area measuring 20*8m. How many centimeters is the height of the resulting layer?

Correct answer:

V =  56 m³
d =  35 cm

Step-by-step explanation:

$$\begin{gathered} a=40\text{dm}\to \text{m}=40:10\text{m}=4\text{m} \\ b=40\text{dm}\to \text{m}=40:10\text{m}=4\text{m} \\ c=350\text{cm}\to \text{m}=350:100\text{m}=3.5\text{m} \\ V=a\cdot b\cdot c=4\cdot 4\cdot 3.5=56{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} x=20\text{m} \\ y=8\text{m} \\ S=x\cdot y=20\cdot 8=160{\text{m}}^2 \\ V=S\cdot d_1 \\ {d}_1=V/S=56/160=\frac{7}{20}=0.35\text{m} \\ d=d_1\to \text{cm}=d_1\cdot 100\text{cm}=0.35\cdot 100\text{cm}=35\text{cm}=35\text{cm} \end{gathered}$$

Try another example