Collin is buying dirt to fill a garden bed that is a 9ft by 16ft rectangle. If he wants to fill it to a depth of 4 inches, how many cubic yards of dirt does he need? If dirt costs $25 per yard cubed, how much will the project cost?

Answer:Cubic yards of dirt needed for project = [tex]1\frac{7}{9}[/tex] cubic yardsCost of Project = About $44.44Step-by-step explanation:To find number of cubic yards of dirt needed, we need to find the volume.Rectangular Prism Volume = length * width * depthNote: Length is 9ft, width is 16ft, depth is 4 inches. We need to change depth to ft. So 4 inches = [tex]\frac{1}{3}[/tex] feet. Now finding the volume (in cubic ft) =  [tex]9*16*\frac{1}{3}=48[/tex]We know 3 feet is  1 yard. To convert cubic feet to cubic yards, we have to divide it by (3)^3 = 27. Hence:[tex]\frac{48}{27}=\frac{16}{9}[/tex] cubic yards* Since dirt is $25 per cubic yard, to find cost, we multiply 25 by 16/9. HenceCost of Project = 25 * 16/9 = 400/9 = $44.44