How many cubic yards of material must be removed for a ditch that is 4.5 feet wide, 6 feet deep, and 120 feet long?

To determine the volume of material that must be removed for the ditch, calculate the volume using the formula for the volume of a rectangular prism, which is length × width × height.

In this case, the dimensions of the ditch are as follows:

• Length is 120 feet

• Width is 4.5 feet

• Depth (or height) is 6 feet

First, calculate the volume in cubic feet:

Volume = Length × Width × Depth

Volume = 120 feet × 4.5 feet × 6 feet

Volume = 120 × 4.5 = 540 cubic feet

Volume = 540 × 6 = 3240 cubic feet

Since the answer choices are in cubic yards, convert cubic feet to cubic yards. There are 27 cubic feet in one cubic yard.

To perform the conversion:

Volume in cubic yards = Volume in cubic feet ÷ 27

Volume in cubic yards = 3240 cubic feet ÷ 27 = 120 cubic yards

Thus, the volume of the material that must be removed for the ditch is 120 cubic yards. This means that the correct answer is indeed the choice indicating 120 cubic yards as it accurately reflects the calculated volume from the given