Math Problem Statement

A container shaped as a rectangular prism can hold 840 wooden cube blocks with edge lengths of 12 ft.

What is the volume of the container?

Enter your answer in the box.

 ft³

Solution

To find the volume of the container, we need to determine the total volume occupied by the 840 wooden cube blocks.

Step 1: Find the Volume of One Cube Block

Each wooden cube has an edge length of 12 ft, so its volume is:

Vcube=side3=123=12×12×12=1,728 ft3V_{\text{cube}} = \text{side}^3 = 12^3 = 12 \times 12 \times 12 = 1,728 \text{ ft}^3

Step 2: Find the Volume of the Container

Since the container holds 840 of these cubes, the total volume is:

Vcontainer=840×1,728V_{\text{container}} = 840 \times 1,728

=1,451,520 ft3= 1,451,520 \text{ ft}^3

Final Answer:

1,451,520 ft3\mathbf{1,451,520} \text{ ft}^3


Would you like a breakdown of multiplication steps? Let me know!

Here are five related questions:

  1. What is the surface area of one wooden cube?
  2. If the container is twice as tall, what would its new volume be?
  3. What are possible dimensions for the container if it is a rectangular prism?
  4. How many wooden cubes would fit if their edge length was 6 ft instead?
  5. If the cubes were stacked in layers, how many layers would there be?

Tip: When solving cube-related problems, always start with volume calculations before considering arrangement possibilities!

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Math Problem Analysis

Mathematical Concepts

Volume of Rectangular Prism
Volume of Cube
Multiplication

Formulas

Volume of Cube: V = side^3
Volume of Container: V = number of cubes × volume of one cube

Theorems

Basic Volume Formula for Rectangular Prisms

Suitable Grade Level

Grades 6-8