Understanding Volume
What is the definition of volume?
Volume is the amount of space in a 3-dimensional object.
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 foot deep?
168 cubic feet
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
How many unit cubes are in the bottom layer of a prism that has a length of 2 and a width of 8 units?
16 unit cubes
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
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.
Parker is using blocks to make a model of a rectangular prism. The first layer has 24 blocks. The finished model will have a total of 10 layers like the base. What will be the volume, in cubic units, of the finished model?
240 cubic units
The toy box Tim made for Greg was 12 inches longer than Tim's toy box, but had the same height and width. If Tim's toy box had a height of 6 inches, a length of 12 inches and a width of 24 inches, what is the volume of Greg's toy box?
20, 736 cubic inches
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
Michelle has 2 small pizza boxes that have a length of 18 inches and width of 7 inches. She has 1 large pizza box that has a length of 24 inches and a width of 8 inches. Both boxes have a height of 2 inches. What is the combined volume if Michelle stacks all three pizza boxes together?
18 x 7 x 2= 252 cubic inches
252 x 2= 504 cubic inches
24 x 8 x 2= 384 cubic inches
504 + 384=
888 total cubic inches
Which of the following items could you find the volume of? A) Lunch Box B) Sheet of paper C) Rug D) Water bottle
A) Lunch Box D) Water bottle
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
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 cubic inches
Once you know how many cubes are in one layer, what else do you need to know to find the volume?
How many layers there are.
Jay created a model of a building from two rectangular prisms. One building had a volume of 15 cubic inches. If the model had a total volume of 34 cubic inches, what was the volume of the other building?
19 cubic inches
Explain how you can use the number of cubes in the base layer to find the volume of any rectangular prism.
You can multiply the base area or number of cubic units in the base by the number of layers (height) to find the total volume.
It takes 16 one-inch cubes to completely cover the bottom of a cereal box without leaving any gaps or overlapping any cubes. If takes a total of 12 layers to fill the entire cereal box,what is the volume, in cubic inches, of the cereal box?
192 cubic inches
What is the volume of a cube with an edge length of 2 feet?
8 cubic feet
Jacob packed four boxes the size of Box A and five boxes the size of Box B into the same large shipping container.
Box A dimensions- 4 x 5 x 20
Box B Dimensions- 3 x 6 x 30
There was no space left over. What is the volume, in cubic inches, of the shipping container?
940 cubic inches
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 1/2 the volume of the pool. What is the total volume of the pool and hot tub?
1,600 cubic feet
A right rectangular prism has a base length of 4 units and a width of 32 units.
Part A. How many unit cubes are needed to make one layer of cubes in the prism?
Part B. If the prism has a height of 12 units, write an expression that can be used to find the volume of the prism.
Part C. Determine the volume of the prism, in cubic units.
Part A= 128 unit cubes
Part B= 4 x 32 x 12
Part C= 1,536 cubic units
A jewelry store uses a large box to hold 1 cubic centimeter boxes of pearls.
Part A. The boxes of pearls are each 1 cm by 1 cm by 1 cm. How many boxes of pearls will fit in the bottom layer of the large box if the box has a length of 3 cm and a width of 4 cm.
Part B. How many total boxes of pearls will fit in the large box if it has a height of 5 cm?
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
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 dimension combinations 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= 5 x 8x3
12 x 2 x 5
5 x 4 x 6
5 x 24 1
Each unit cube has side lengths of 1 inch.
Part A. What is the volume of the prism, in cubic inches if its height is 7 inches, its length is 4 inches and its width is 3 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
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