Volume

Understanding Volume

100

What is the definition of volume?

Volume is the amount of space occupied by a 3-dimensional object.

200

Explain the difference between 12 square units and 12 cubic units.

12 square units describes the area of a 2-dimensional figure. Is is the area covered by 12 squares that are 1 unit long. 12 cubic units describes the volume of a 3-dimensional figure that holds exactly 12 cubes whose edges are 1 unit long.

300

What are some items you might want to find the volume of? A) Lunch box B) Baking pan C) Bedroom D) Water bottle

A) Lunch box B) Baking pan D) Water bottle

400

Explain how you can use multiplication to find the volume of any rectangular prism.

First, you can multiply the length by the width to find how many cubes are in 1 layer. Then you can multiply by the number of layers (height) to find the total volume.

500

A right rectangular prism is shown. Part A. How many unit cubes are needed to make one layer of cubes in the prism? Explain your answer. Part B. Write an expression that can be used to find the volume of the prism. Explain how this expression compares with the number of unit cubes that would fit in the prism. Part C. Determine the volume of the prism, in cubic units.

Part A= 128 unit cubes Part B= 16 x 8 x 12 This formula compares to the number of unit cubes that would fit in the prism as this is the formula for volume (how much space is inside the figure). Part C= 1,536 cubic units

Recognizing Volume as an Attribute of Solid Figures

100

Sebastian is building a deck in his backyard. How many cubic feet of cement does Sebastian need to order for a concrete deck that is 12 feet wide, 14 feet long, and 1/2 foot deep?

84 cubic feet

200

Parker is using blocks to make a model of a rectangular prism. The first layer of blocks is shown below. The finished model will have a total of 10 layers like the one shown above. What will be the volume, in cubic units, of the finished model?

240 cubic units

300

Mariah used unit cubes that were each 1 inch long, 1 inch wide, and 1 inch tall to make a right rectangular prism. When finished, the prism measured 30 inches long, 15 inches wide, and 12 inches tall. What was the total number of unit cubes used to make the prism?

5,400 cubic inches

400

It takes 16 one-inch cubes to completely cover the bottom of a cereal box without leaving any gaps or overlapping any cubes. The picture represents one layer of 16 cubes covering the bottom of the cereal box. It takes a total of 12 layers of 16 cubes to fill the entire cereal box. What is the volume, in cubic inches, of the cereal box?

192 cubic inches

500

This figure shows a large box the jewelry store uses to hold 1 cubic centimeter boxes of pearls. Part A. The boxes of pearls are each 1 cm by 1 cm by 1 cm. Show or explain how many boxes of pearls will fit in the bottom layer of the large box. Part B. How many total boxes of pearls will fit in the large box? Part C. The jewelry store owner has another large box with the same bottom layer as the box shown. If he wants to fit 108 of the pearl boxes in the second large box, what would its height have to be?

Part A= 12 boxes of pearls Part B= 60 boxes of pears Part C= 9 cm

Formula

100

Pattie got a package in the mail. The package was in the shape of a rectangular prism. The base was in the shape of a square with a length of 8 inches. The height of the package was 5 inches. What is the volume of the package in cubic inches?

320 cubic inches

200

The toy box Tim made for Greg was 12 inches longer than Tim's toy box, but had the same height and volume. What was the width of the toy box Tim built for Greg? What is the volume of Tim's first toy box, in cubic inches?

10,368 cubic inches

300

A gardener has built a rectangular prism shaped planter box to plant a row of flowers. The box is 8 inches tall, 10 inches wide, and 30 inches long. How many cubic inches of soil are needed to completely fill this planter box?

2,400

400

What is the volume of a cube with an edge length of 2 feet?

8 cubic feet

500

Rhonda needs to buy a box that has a volume equal to 120 cubic feet. She would like to buy a box that has one measurement equal to 5 feet. Part A. If Rhonda does buy a box with a volume of 120 cubic feet, how could the remaining measurements be found? Part B. What are two other possible measurements for a box with a volume of 120 cubic feet and one measurement of 5 feet?

Part A= L x W x H= 120 cubic feet Part B= Answers will vary

Counting Unit Cubes

100

How many unit cubes are in the bottom layer of this prism?

16 unit cubes

200

Ciara is packing her baby brother's blocks into a box that has a volume of 24 cubic inches. The box is 3 inches tall. What could be the length and width of the box? A) 8 inches long, 3 inches wide B) 8 inches long, 1 inch wide C) 12 inches long, 2 inches wide D) 4 inches long, 2 inches wide

B) 8 inches long, 1 inch wide, 3 inches tall= 24 cubic units D) 4 inches long, 2 inches wide, 3 inches tall= 24 cubic units

300

Once you know ho many cubes are in one layer, what else do you need to know to find the volume?

How many layers there are.

400

The dimensions of two different boxes are shown in the picture below. Jacob packed four boxes the size of Box A and five boxes the size of Box B into the same large shipping container. There was no space left over. What is the volume, in cubic inches, of the shipping container? Show or explain your work.

3,500 cubic inches

500

Each unit cube has side lengths of 1 inch. Part A. What is the volume of the prism, in cubic inches? Part B. Raj added 3 more layers to the top of the prism. What is the volume of the new prism, in cubic inches?

Part A) 84 cubic inches Part B) 120 cubic inches

Additive Volume

100

Chancy made a 2-layer cake. Each layer is a 3 inch high rectangular prism. The base of the bottom layer is 120 square inches. The base of the top layer is 84 square inches. What is the total volume of the cake?

612 cubic inches

200

The diagram shows the design of a custom aquarium. The aquarium is made up of rectangular prisms. What is the total volume, in cubic feet, of the aquarium?

28

300

Jay created a model of a building from two rectangular prisms. What is the total volume of the model of the building, in cubic inches?

34 cubic inches

400

A pool shaped like a rectangular prism is 40 feet long, 20 feet wide, and 4 feet deep. Attached to the pool is a hot tub with 1/4 the volume of the pool. What is the total volume of the pool and hot tub?

4,000 cubic feet

500

A construction crew is building homes for a housing development. The crew has plans for two different types of homes, two-story houses and duplexes. Part 1. The plan for a two-story house calls for two rectangular prisms. One makes up the main floor and the other is the second floor. The prism for the main floor is 36 feet (ft) long, 28 ft wide, and 10 ft high. The second-floor prism is 22 ft long, 28 ft wide, and 10 ft high. What is the total volume of the house? Part 2. A duplex is a term for two separate homes built in one building. A duplex in the housing development consists of two identical rectangular prisms stacked. The height of each home is exactly half of the total height of the building. Each unit of the duplex is 40 ft long and 26 ft wide. If the volume of the entire two-story building is 16,640 cubic ft, what is the height of each home?

Part 1= 16,960 cubic feet Part 2= 8 cubic feet