For excavation of a house that is 35' wide, 44' long, and 21" deep, how many cubic yards of dirt need to be excavated when rounded to the next whole yard?

To determine the volume of dirt that needs to be excavated, you begin by calculating the volume in cubic feet and then convert that volume to cubic yards.

First, the formula for volume is length × width × depth. In this case, the dimensions of the house are given as follows: the width is 35 feet, the length is 44 feet, and the depth is 21 inches. To use these measurements consistently, it's advisable to convert the depth from inches to feet. Since there are 12 inches in a foot, 21 inches is equal to 21/12 feet, which simplifies to 1.75 feet.

Now, plug the dimensions into the volume formula:

[

Volume = Length × Width × Depth

]

[

Volume = 44 feet × 35 feet × 1.75 feet

]

Calculating this gives us:

[

Volume = 44 × 35 = 1540

]

[

1540 × 1.75 = 2695 \text{ cubic feet}

]

Next, to convert cubic feet to cubic yards, remember that there are 27 cubic feet in a cubic yard. Therefore, divide the total cubic feet by 27:

[