How many cubic yards of gravel are needed to fill a ditch 3 feet deep, 10 feet wide, and 12 feet long with 18 inches of gravel?

To calculate the amount of gravel needed, it's essential to first figure out the total volume of the ditch that needs to be filled with gravel. Given the dimensions, the ditch is 3 feet deep, 10 feet wide, and 12 feet long, but you only need to fill it with 18 inches of gravel.

Start by converting all measurements to the same unit. Since the gravel depth is given in inches, convert 18 inches to feet:

[

18 \text{ inches} = 1.5 \text{ feet}

]

Next, calculate the volume of gravel needed using the formula for volume, which is length × width × height:

[

\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}

]

Substituting the dimensions specific to the gravel:

[

\text{Volume} = 12 \text{ ft} \times 10 \text{ ft} \times 1.5 \text{ ft}

]

Calculating this gives:

[

\text{Volume} = 12 \times 10 \times 1.5 = 180 \text{ cubic feet}

]