The volume of Rectangular Prism
How can you use a formula to find the volume of a rectangular prism?
Remember that volume is the number of cubic units needed to pack a solid figure without gaps or overlaps.
Find the volume of the rectangular prism if each cubic unit represents 1 cubic foot.
You can find the volume of a rectangular prism by counting cubes or using a formula.
A formula is a rule that uses symbols to relate two or more quantities.
How can you measure space inside a solid figure?
Volume is the number of cubic units needed to pack a solid figure without gaps or overlaps. A cubic unit is the volume of a cube measuring 1 unit on each edge.
What is the volume of this rectangular prism?
Each cube of a solid figure is 1 cubic unit.
If the dimensions of a rectangular prism are given as length l, width w, and height h, then use this formula to find the volume v.
Volume = length x width x height
V = l x w x h
Q. 1. A wooden block measures 5 centimeters tall, 3 centimeters wide, and 2 centimeters long. The area of the base is 6 cm. Draw a rectangular prism to show the block and label it. What is the volume of the block?
Q.2. The dictionary is 3 inches thick. What is the volume of the dictionary?
Q.3. The perimeter of an equilateral triangle is 51 feet. What is the length of one of its sides? Explain your work.
Q.4. Harry is in line at the store. He has three items that cost $5.95, $4.25, and $1.05. Explain how Harry can add the cost of the items mentally before he pays for them.
Q.5. Ariel is thinking of a three-dimensional figure that is made by combining two rectangular prisms. What is the volume of this three-dimensional figure?
You can find the volumes of the rectangular prisms that make up the solid figure. Show your work!
Q.6. The shape and size of a storage building are shown in the figure. The building supervisor wants to find the volume to determine how much storage space is available. What is the volume of the building?
You can find the volume of this figure by finding the volume of two rectangular prisms that make up the figure.
Q.7. The building can be separated into two rectangular prisms as shown. Identify the measurements for the length, width, and height of each prism.
Use the formula v = l.w.h to find the volume of each rectangular prism.
Volume of Prism A
V = l.w.h
= 5 x 3 x 3
= 45
Volume of Prisms B
V = l.w.h
= 3 x 1 x 4
= 12
Add to find the total volume
45 + 12 = 57
The volume of the storage building is 57 cubic meters.
Which tools can I use?
Ans: Tools such as place value blocks, cubes and grid paper can help you solve problems involving volume.
Q. 8. A school has two wings, each of which is a rectangular prism. The school district is planning to install air conditioning in the school and needs to know its volume. What is the volume of the school? Solve this problem any way you choose.
* Model with Math Write a multiplication expression for the volume of each wing of the building.
* Write a mathematical expression that can be used to find the total volume of the school.
* How can you use Volume Formulas to solve Real-World Problems?
Q. 9. The nature center has a large bird cage called an aviary. It consists of two sections, each shaped like a rectangular prism. There need to be 10 cubic feet of space for each bird. How many birds can the nature center have in the aviary?
* You can make sense of the problem by breaking it apart into simpler problems.
Find the volume of each section. Use the formula
V = l . w. h
Small section:
V = 4 . 3. 8
= 96
Large section:
V = 10 . 6. 8
= 480
Add to find the total volume:
96 + 480 = 576
The combined volume is 576 cubic feet.
Divide to find the number of birds that will fit.
576 cubic feet
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10 cubic ft
576 ➗ 10 = 57.6
The nature center can put 57 birds in the aviary.
Q.10. A floor plan of Angelica's bedroom and closet is shown at the right. The height of the bedroom is 8 cm. The height of the closet is 4 cm. What is the total volume of the bedroom and the closet?
Does it make sense for Angelica to find the combined area of the bedroom floor and closet floor before finding the total volume? Explain your thinking.
