Toss coconut with food coloring until evenly tinted, set aside.
Place cake on large serving plate. Frost the top and side with whipped topping, sprinkle with coconut.
Cut cake into 8 slices, leaving all slices in place. Carefully pull out cake slices and separate slightly to resemble the petals of an open flower. Spoon 3 cups of strawberries into center of "flower". Store the leftover cake in refrigerator.