First of all we need to realize that half of a yard is as much as 18 inches. If a diameter of the circle is 18 inches, then its radius is 18 ÷ 2 = 9 inches.
If there are 4 dogs and they each eat 2 pounds of food each day. Then, all together there are 8 pounds of food getting eaten each day. You will want to divide 456 by 8.
456/8= 57 days.
456 punds of dog food will last 57 days for 4 dogs.