What is the volume of the box if the original length of each side of the cardboard...
Check the final answer first, then review the worked steps.
Problem
What is the volume of the box if the original length of each side of the cardboard was 9 inches?
Answer
729
Step-by-step solution
- Identify the shape and formula: The problem asks for the volume of a box. A box is a rectangular prism. The volume of a rectangular prism is given by the formula $V = lwh$, where $l$ is the length, $w$ is the width, and $h$ is the height.
- Determine the dimensions: The problem states that the original length of each side of the cardboard was 9 inches. Since it's a square piece of cardboard, the length and width of the base of the box are determined by how it's folded. However, the question implies a simple cube if no cuts or folds are specified. If the cardboard itself forms the box without any cuts or modifications, and the original length of each side was 9 inches, it suggests a cube with side length 9 inches.
3. Calculate the volume: Using the formula for the volume of a cube, which is $V = s^3$ (where $s$ is the side length), we substitute the given side length:
$V = 9^3$
$V = 9 \times 9 \times 9$
$V = 81 \times 9$
$V = 729$
The volume is in cubic inches since the side length is in inches.