Answer :

First we convert each measurement of feet into yards using yd = (1/3)*ft which gives us a hole 2 yards deep, 4 yards wide, and 5 yards long. To calculate the amount of dirt removed, we can simply find the volume of the hole using width*depth*length which is 2*4*5, so the answer is 40 cubic yards.
semsee45

Answer:

40 cubic yards

Step-by-step explanation:

To determine how many cubic yards of dirt were removed from the hole, we can model the hole as a rectangular prism with the following dimensions:

  • Width w = 12 ft
  • Length l = 15 ft
  • Height h = 6 ft

Since we need to find the volume of the prism in cubic yards, yet the dimensions are given in feet, we should first convert the lengths from feet to yards by dividing each by 3, as there are 3 feet in 1 yard:

[tex]w=\dfrac{12}{3}=4\; \textsf{yd}\\\\\\l=\dfrac{15}{3}=5\; \textsf{yd}\\\\\\h=\dfrac{6}{3}=2\; \textsf{yd}[/tex]

Now, we can use the formula for the volume of a rectangular prism to find the volume of removed dirt:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Rectangular Prism}}\\\\V=w\times l \times h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$w$ is the width of the base.}\\\phantom{ww}\bullet\;\textsf{$l$ is the length of the base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]

Therefore:

[tex]\textsf{Volume of removed dirt}=4 \times 5 \times 2\\\\\textsf{Volume of removed dirt}=40\; \sf yd^3[/tex]

So, 40 cubic yards of dirt was removed.

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