Bake Sale Fudge Boxes: Counting Cubic Units

Pack boxes with unit cubes to find their volume.

Part 1: Count the Fudge Cubes

The class cuts fudge into unit cubes for the bake sale. Each fudge cube is 1 inch long, 1 inch wide, and 1 inch tall, so it has a volume of 1 cubic inch. Each box is packed full with no gaps or overlaps. Some cubes are hidden behind others.

Priya packs one layer of fudge cubes in a tray.

How many fudge cubes are in the tray? cubes
What is the volume of the fudge in the tray? cubic inches

What is the volume of the fudge in this box?

cubic inches

What is the volume of the fudge in this box?

cubic inches

Which way of finding the volume of this box of fudge is correct?

A. Add the edges: 3 + 3 + 3 = 9 cubic inchesB. Count only the cubes you can see: 19 cubic inchesC. Count by layers: 3 layers of 9 cubes = 27 cubic inchesD. Count the squares on all 6 faces: 54 cubic inches

Part 2: Fill the Gift Boxes

Marco is packing fudge cubes into gift boxes. The dashed lines show the empty part of each box. Each box will be packed full with no gaps or overlaps.

Marco has packed the bottom layer of this box.

How many fudge cubes are in the box now? cubes
How many more fudge cubes does Marco need to fill the box? cubes
What is the volume of the box when it is full? cubic inches

Marco has packed 2 layers of this box.

How many more fudge cubes does Marco need to fill the box? cubes
What is the volume of the box when it is full? cubic inches

This tall box has only its bottom layer packed. What is the volume of the box when it is full?

cubic inches

Part 3: Think About Packing

Answer each question about packing boxes with unit cubes.

Ava packs a box full with 16 fudge cubes. There are no gaps or overlaps. What is the volume of the box?

A. 16 square inchesB. 16 cubic inchesC. 16 inchesD. 4 cubic inches

Theo puts 15 unit cubes inside a box. He leaves empty gaps between some of the cubes. Which statement about the volume of the box is true?

A. The volume is exactly 15 cubic units.B. The volume is less than 15 cubic units.C. The volume is more than 15 cubic units.

10.

Each box is packed full of unit cubes with no gaps or overlaps. Match each box to its volume.

11.

Jada packs a box full with 12 unit cubes, with no gaps or overlaps. She says the volume of the box is 12 square units. Explain her mistake and write the correct volume.