How many cubic yards of gravel will be needed?

Question

A driveway is 36ft long and 10ft wide, and will be covered in gravel that is 2in deep.

Answer 1

To convert units without changing the value, we use the Multiplicative Identity (that is, 1).

 

Volume of gravel needed:

   (36ft)*(10ft)*(2in)

   (36ft)*(10ft)*(2in)*1*1*1

   (36ft)*(10ft)*(2in)*((1 yd)/(3 ft))*((1 yd)/(3 ft))*)((1 yd)/36 in))

   (36)*(10)*(2)*(1/3)*(1/3)*(1/36)   yd³      

                [note: ft and in cancel, leaving only yd, yd, yd]

                [additional note:  I write this way to paste into Excel]

    20/9 yd³

    2 2/9 yd³

 

Answer 2

Michael has the right answer but it may be easier

to follow if you convert all units to yards first

and then do one straight multiplication for

Length*Width*Height

 

(36 ft)(1/3 yd/ft) = 12 yds in length

(10 ft)(1/3 yd/ft) = 10/3 yds in width

(2 in)(1/12 ft/in)(1/3 yd/ft) = 1/18 yds depth (height)

 

L*W*H = 12(10/3)(1/18) = 40/18 = 2 2/9 cubic yards

 

Answer 3

Finding cubic yards means to find the volume in yards.  The dimensions that are given are in different units.  We need to convert them so that the units are consistent.  Since 2 of the dimensions are in feet, we will convert all the dimensions to feet.

 

Use the conversion factor

 

12 inches = 1 foot

 

2 in = 1/6 ft

 

 

Now we can multiply the dimensions to get the volume in feet.

 

Volume = 36ft × 10ft × (1/6)ft

            = 60ft³

 

Now, we can convert feet to yards using the conversion factor

 

3 ft = 1 yd

 

 

Cube both sides of the conversion to get the conversion factor for cubic yards.

 

27ft³ = 1 yd³

 

Using this new conversion factor, set a proportion to convert 60ft³ to a value in cubic yards.

 

27 / 60 = 1 / x

 

where x is the value in cubic yards.

 

 

Cross multiply.

 

27x = 60

 

 

Divide both sides of the equation by 27.

 

x = 60 / 27

 

x = 20 / 9

 

 

Convert this to a mixed number.

 

x = 2 2/9

 

 

2 2/9 cubic yards of gravel will be needed.