a worker dig a ditch with perpendicular sides.It is 1.05m wide at the top and at the bottom. If it is 1.80m deep and 21.6m long.How many cubic metres of earth are removed?[give your answer to 1 decimal place.]
1.05x1.80x21.6=40.824
40.8 cubic meters of earth removed
To calculate the volume of the ditch, we need to multiply the area of its cross-section by its length.
First, let's find the area of the cross-section of the ditch. Since the ditch has perpendicular sides, the shape of the cross-section is a trapezoid. We can calculate the area of a trapezoid using the formula:
Area = (a + b) * h / 2
where "a" and "b" are the lengths of the parallel sides of the trapezoid, and "h" is the height (or width) of the trapezoid.
In this case, the top width (a) is 1.05 m and the bottom width (b) is also 1.05 m. The height (h) is given as the depth of the ditch, which is 1.80 m.
Now, let's calculate the area of the cross-section:
Area = (1.05 + 1.05) * 1.80 / 2
= 2.10 * 1.80 / 2
= 3.78 m² (rounded to two decimal places)
Next, we multiply the area of the cross-section by the length of the ditch to find its volume:
Volume = Area * Length
= 3.78 m² * 21.6 m
= 81.648 m³ (rounded to one decimal place)
Therefore, approximately 81.6 cubic meters of earth are removed to dig the ditch.