Understanding Volume
What is the definition of volume?
Volume is the measurement of the amount of space in a 3-dimensional object/solid figure.
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
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
Find the volume:
Length:2 Width:7 Height:4
56 cubic units
Explain the difference between 12 SQUARE units and 12 CUBIC units.
12 square units describes the area of a 2-dimensional figure. 12 cubic units describes the volume of a 3-dimensional figure.
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
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
Mike built a model tool chest out of unit cubes. The model had a length of 12 cubes, the width of 7 cubes, and 6 layers. What is the volume of his model?
504 cubic units
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
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.
A desk measured 16 cubic inches across, 5 cubic inches high, and 7 cubic inches wide. Find the volume.
560 in3
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 it 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
Jacob packed four boxes that totaled the size of Box A and five boxes that totaled 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
Lisa measured the aquarium in her den. It measured 14 feet long, had a height of 4 feet, and was 3 feet wide.
A. What is the Base X Height formula Lisa used?
B. What was the measurement that Lisa came up with?
A. 42 feet square X 4 feet
B. 168 feet3
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 OR 128 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
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
Ms. Freeman built a flower pot with 1 inch cubes. She stacked 6 cubes. Then she counted out 5 cubes from left to right and 4 cubes from front to back.
EXPLAIN how did she find her formula and tell what the formula was?
Ms. Freeman multiplied the 5 cubes by the 4 cubes and got 20 inches2. Then she multiplied 20 inches2 by 6 cubes and got 120 inches3 as the volume.