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

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