colin is buying dirt to fill a garden bed that is a 9 foot by 16 foot 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, how much will the project cost?
just keep track of the units so you can convert volume to dollars:
9ft * 16ft * 4in * ft/12in * yd^3/27ft^3 * $25/yd^3 = $44.44
To find the number of cubic yards of dirt Colin needs, we need to calculate the volume of the garden bed. The formula for the volume of a rectangular prism (the shape of the garden bed) is length × width × height.
First, let's convert the dimensions into yards. Since 1 yard is equal to 3 feet, we divide the length and width by 3:
Length = 9 feet ÷ 3 = 3 yards
Width = 16 feet ÷ 3 = 5.33 yards (rounded to two decimal places)
Next, we need to convert the depth from inches to yards. Since 1 yard is equal to 36 inches, we divide the depth by 36:
Depth = 4 inches ÷ 36 = 0.11 yards (rounded to two decimal places)
Now we can calculate the volume of the garden bed:
Volume = Length × Width × Depth
= 3 yards × 5.33 yards × 0.11 yards
≈ 0.18 cubic yards (rounded to two decimal places)
Therefore, Colin needs approximately 0.18 cubic yards of dirt to fill the garden bed to a depth of 4 inches.
To calculate the cost of the project, we multiply the number of cubic yards of dirt by the cost per yard. In this case, the cost is $25 per yard:
Cost = Volume × Cost per yard
= 0.18 cubic yards × $25 per yard
= $4.50
Therefore, the project will cost approximately $4.50.