What is the length of material in yards delivered by a roll with a speed of 290 rpm and a diameter of 46 mm? (Note: assume the roll turns for 90 seconds.)

Answer:The length of material is 68.7 yards.Step-by-step explanation:If the material is delivered in a roll, we can calculate how many material is delivered by turn (one rotation). In one turn it delivers (π*D) of material, its perimeter.If the diameter is 46 mm, in one turn the material delivered is[tex]m=(\pi*D)=3.14*46mm=144.44 mm/rev[/tex]As we know the rotational speed, we can calculate the amount of material delivered by unit of time:[tex]m=144.44 \frac{mm}{rev}*290\frac{rev}{min}=  41,887.6\frac{mm}{min}[/tex]If the roll turns for 90 seconds (or 1.5 min) we can calculate[tex]m=41,887.6\frac{mm}{min}*1.5min=62,831.4mm[/tex]As we need the result in yards, we can convert (1 yard=914.4 mm)[tex]m=62,831.4mm*\frac{1yard}{914.4mm} =68.7 \,yards[/tex]