11-29. Rosilaine is ordering wood chips to cover her dog run area. The size of the dog run is 9.5 feet by 12 feet and she wants the wood chips to be 4 inches deep. The wood chips are sold by the cubic yard at the landscaping supply store.

See the calculations, explanations and results below.

1) The section to cover has tha shape of box with these dimensions:

length: 9.5 ft

width: 12 ft

depth: 4 inches

3) The volume of a box is calculated as:

V = length * witdth * depth

Since the depth is in inches convert to feet.

Conversion factor: 1 feet = 12 inches

⇒ depth = 4 in * 1 feet / 12 inches = 1/3 feet

Now, calculate the volume using feet:

V = 9,5 feet * 12 feet * 1/3 feet = 38 feet³

4) convert that to yard³ to compare with the calculations made by Rosilaine:

Conversion factor: 1 yard = 3 feet

⇒ 38 ft³ * (1 yard / 3 ft) ³ = (38 / 27) yard³ = 1.41 yard³

5) The error probably was that Rosailined used a wrong conversion factor.

Notice that 38 / 3 ≈ 12.7; so a likely mistake is that she did not cube the factor and so got about 12 yard³.

6) She might order 1.5 yard³ or 2.0 yard³ depending on the seller's rates and restrictions. With that she will have enough and will not have too much left over.