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1. Matthew is at the beach with his family. He is using a rectangular prism-shaped container to mold sand for his sandcastle. The container has the following dimensions: 12 in. by in. by in.
(a) Matthew noticed that the container was one-fourth full of sand. How many more cubic inches of sand would be required to fill the container? Show your work.
(b) Matthew’s father has a container that has dimensions that are each double the dimensions of Matthew’s container. Matthew thought that the volume would also double. Is Matthew correct? How many times greater is the volume of the larger container than the volume of the smaller one? Show your work and explain your reasoning.
2. Jasmine is making a 3-tiered wedding cake. The cake is made up of 3 rectangular prisms. The bottom tier has a width of 16 in, a length of 16 in, and a height of in. The middle tier has the same height as the bottom tier but has a width and length that are each of the dimensions of the bottom tier. The top tier also has the same height as the bottom tier, but its width and length are each of the dimensions of the middle tier. Jasmine has made enough batter for 2,200 in3 of cake. Does Jasmine have enough batter to make this cake? Explain and show your work.
3. A rectangular prism has dimensions of , 2, and in. (a) Determine the edge length of the largest unit cube that you could use to pack the prism. Explain. (b) What is the volume of the prism? Explain. (c) How many cubes with the edge length from part (a) will fit into the prism? Explain.
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