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Layer Cakes and Bread Boxes: Adding Volumes at the Bakery

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Layer Cakes and Bread Boxes: Adding Volumes at the Bakery

Find the volume of each rectangular prism, then add the two volumes.

Layer by layer

Each solid is made of two rectangular prisms that do not overlap. Find the volume of each prism, then add.

1.
Rosa bakes a two-layer cake. The bottom layer is 12 inches long, 9 inches wide, and 2 inches tall. The top layer is 8 inches long, 6 inches wide, and 2 inches tall.

Bottom layer: cubic inches
Top layer: cubic inches
Whole cake: cubic inches

2.
Theo builds a tiny model of the bakery counter out of sugar cubes. Each sugar cube is 1 cubic inch. One part of the counter is 5 cubes long, 3 cubes wide, and 2 cubes tall. The other part is 4 cubes long, 2 cubes wide, and 2 cubes tall. How many sugar cubes does Theo use in all?

sugar cubes

3.
The bakery's bread box has a big bottom part and a small shelf on top. The bottom part is 15 inches long, 10 inches wide, and 4 inches tall. The shelf is 15 inches long, 4 inches wide, and 3 inches tall.

Volume of the bread box = cubic inches

4.
The glass display case is shaped like the letter L. It can be split into two prisms that are both 3 feet tall. One prism is 7 feet long and 2 feet wide. The other prism is 4 feet long and 2 feet wide.

Volume of the display case = cubic feet

Choose and compare

All lengths are in inches. Each cake or box is made of two rectangular prisms that do not overlap.

5.
A square cake has a bottom layer that is 10 by 10 by 3 and a top layer that is 6 by 6 by 3. Which expression gives the volume of the whole cake?
Question 5 options
6.
Each two-layer cake is made of the two prisms listed. Match each cake to its total volume.
7.
Mr. Patel makes gift boxes by gluing two boxes together. He needs a gift box that holds exactly 150 cubic inches. Circle every gift box that works.

8.
Cake A has layers that are 12 × 8 × 2 and 6 × 4 × 2.
Cake B has layers that are 10 × 10 × 2 and 5 × 4 × 2.
Which cake has the greater volume?
Question 8 options

Solve and explain

Show your work. Label every answer in cubic units.

9.
The bakery's flour bin has two parts that do not overlap. Together they hold 1,040 cubic inches of flour. The first part is 10 inches long, 8 inches wide, and 6 inches tall. What is the volume of the second part?

Second part: cubic inches

10.
The walk-in cooler has a main room that is 8 feet long, 6 feet wide, and 7 feet tall. A small closet joined to it is 3 feet long, 2 feet wide, and 7 feet tall. What is the total volume of the cooler?

Total volume: cubic feet

11.
A cake has a bottom layer that is 8 inches long, 6 inches wide, and 3 inches tall, and a top layer that is 4 inches long, 3 inches wide, and 3 inches tall. Jada adds the lengths (8 + 4 = 12), the widths (6 + 3 = 9), and the heights (3 + 3 = 6). Then she finds 12 × 9 × 6 = 648 cubic inches. Is Jada right? Find the correct volume and explain.