Question

After excavating a lot, workers removed an estimated 7,000 cubic yards of dirt from the area. If this dirt were spread in an even layer over an empty lot with dimensions 30 yards by 64 yards, about how deep, in yards,  would the layer of dirt be? Can you help me with this?

Answer 1

To calculate the depth of dirt spread evenly over a lot, divide the total volume of dirt by the area of the lot. For 7,000 cubic yards of dirt over a lot with an area of 1,920 square yards, the depth would be approximately 3.6458 yards.

Step-by-step explanation:

To find out how deep the layer of dirt would be if spread evenly over an empty lot that measures 30 yards by 64 yards, we need to calculate the volume of the lot and then divide the amount of dirt by this volume. The volume (V) of a rectangular prism (which, in this case, is our layer of dirt) is found by multiplying its length (L), width (W), and height (H): V = L × W × H.

First, we find the area of the lot: A = L × W = 30 yards × 64 yards = 1,920 square yards. The estimated removed dirt is 7,000 cubic yards. To find the depth, we set up the equation 7,000 cubic yards = 1,920 square yards × depth in yards. Solving for the depth, we find depth = 7,000 cubic yards / 1,920 square yards = approximately 3.6458 yards deep.

Answer 2

`V=7,000\ yd^3\ \ \ and\ \ \ V=30\ yd\ \cdot64\ yd\ \cdot x\\ \\30\cdot64\cdot x=7,000\ /:(30\cdot64)\\ \\x= (7\cdot25\cdot4\cdot10)/(3\cdot10\cdot16\cdot4) \\ \\x= (7\cdot25)/(3\cdot16) \\ \\x= (175)/(48)\ [yd] \ \ \ and\ \ \ 1\ yd=36\ in\\ \\(175)/(48)\ yd =(175)/(48)\cdot 36\ in= (175\cdot3)/(4)\ in=131.25\ in`