What is the maximum number of pieces of 5 cm x 5 cm x 10 cm cake that can be cut from a big cake of 5 cm x 30 cm x 30 cm size?

To find the maximum number of pieces, we divide the volume of the big cake by the volume of one small piece, while ensuring the dimensions fit physically. First, calculate the volume of the big cake: 5 cm x 30 cm x 30 cm = 4500 cubic cm. Next, calculate the volume of one small piece: 5 cm x 5 cm x 10 cm = 250 cubic cm. Divide the total volume by the piece volume: 4500 divided by 250 = 18. Physically, since the height of both the big cake and the small pieces is 5 cm, we only need to look at the 30 cm x 30 cm surface area. We can fit six 5 cm widths along one 30 cm side and three 10 cm lengths along the other 30 cm side. Multiplying 6 by 3 gives exactly 18 pieces with no wastage. Therefore, option C is correct.