Question

In American football, the playing field is 53.33 yards (yd) wide by 120 yards (yd) long. For a special game, the field staff want to paint the playing field orange. Of course, they will use biodegradable paint available for purchase in 25-gallon (gal) containers. If the paint is applied in a thickness of 1.2 millimeters (mm) in a uniform layer, how many containers of paint will they need to purchase?

Answer 1

Answer: 68 containers of paint.

Explanation:

First, we need to make the conversion from milimeters to yards. Knowing that:

`1\ yd=914.4\ mm`

We get:

`(1.2\ mm)((1\yd)/(914.4\ mm))=1.31*10^(-3)\ yd`

Knowing that the playing field is 53.33 yards wide by 120 yards long, and the paint will be applied in a thickness of 1.2 millimeters (
`1.31*10^(-3)\ yd`) , we can find the volume:

`V=(53.33\ yd)(120\ yd)(1.31*10^(-3)\ yd)=8.38\ yd^3`

Now we must make the conversion from cubic yards to gallons. Since
`1\ yd^3=201.974\ gal`, we get:

`(8.38\ yd^3)(((201.974\ gal)/(1\ yd))= 1,692.54\ gal`

To find the number of containers of paint they will need to purchase, we must divide
`1,692.54\ gal` by
`25\ gal`:

`number\ of\ containers=(1,692.54\ gal)/(25\ gal)=67.70\approx68`