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Volume of Rectangular Prisms Word Problems

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Videos, examples, solutions, and lessons to help Grade 5 students learn how to solve word problems involving the volume of rectangular prisms with whole number edge lengths.

New York State Common Core Math Module 5, Grade 5, Lesson 7

Common Core Standards: 5.MD.3, 5.MD.5

Lesson 7 Problem Set

Geoffrey builds rectangular planters.
1. Geoffrey's first planter is 8 feet long and 2 feet wide. The container is filled with soil to a height of 3 feet in the planter. What is the volume of soil in the planter? Explain your work using a diagram.
2. Geoffrey wants to grow some tomatoes in four large planters. He wants each planter to have a volume of 320 cubic feet, but he wants them all to be different. Show four different ways Geoffrey can make these planters, and draw diagrams with the planters' measurements on them.
3. Geoffrey wants to make one planter that extends from the ground to just below his back window. The window starts 3 feet off the ground. If he wants the planter to hold 36 cubic feet of soil, name one way he could build the planter so it is not taller than 3 feet. Explain how you know.
4. After all of this gardening work, Geoffrey decides he needs a new shed to replace the old one. His current shed is a rectangular prism that measures 6 feet long by 5 feet wide by 8 feet high. He realizes he needs a shed with 480 cubic feet of storage.
a. Will he achieve his goal if he doubles each dimension? Why or why not?
b. If he wants to keep the height the same, what could the other dimensions be for him to get the volume he wants?
c. If he uses the dimensions in Part (b), what could be the area of the new shed's floor?

Lesson 7 Homework

This video shows how to find volume of a given rectangular prism. It also explores finding multiple examples of rectangular prisms given a set volume.
Wren makes some rectangular display boxes.
1. Wren’s first display box is 6 inches long, 9 inches wide, and 4 inches high. What is the volume of the display box? Explain your work using a diagram.
2. Wren wants to put some artwork into three large display boxes. She knows they all need a volume of 60 cubic inches, but she wants them all to be different. Show three different ways Wren can make these boxes by drawing diagrams and labeling the measurements.
3. Wren wants to build a box to organize her scrapbook supplies. She has a stencil set that is 12 inches wide that needs to lay flat in the bottom of the box. The supply box must also be no taller than 2 feet. Name one way she could build a toy box with a volume of 72 cubic inches.
4. After all of this organizing, Wren decides she also needs more storage for her soccer equipment. Her current storage box measures 1 foot long by 2 feet wide by 2 feet high. She realizes she needs to replace it with a box with 12 cubic feet of storage, so she doubles the width.
a. Will she achieve her goal if she does this? Why or why not?
b. If she wants to keep the height the same, what could the other dimensions be for a 12-cubic-foot storage box?
c. If she uses the dimensions in Part (b), what is the area of the new storage box’s floor?
d. How has the area of the bottom in her new storage box changed? Explain how you know.

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