If this rectangular prism was filled completely with 1 by 1 unit cubes, what would the volume be?
Understand the Problem
The question is asking to calculate the volume of a rectangular prism that is filled with 1 by 1 unit cubes, requiring an understanding of geometric volume calculation.
Answer
The volume is \( 27 \) cubic units.
Answer for screen readers
The volume of the rectangular prism is ( 27 ) cubic units.
Steps to Solve
- Identify the dimensions of the rectangular prism
From the drawing, observe the dimensions of the rectangular prism. Let's label the dimensions: the height is 3 units, the width is 3 units, and the depth is 3 units.
- Calculate the volume of the rectangular prism
The formula for the volume ( V ) of a rectangular prism is given by:
$$ V = \text{length} \times \text{width} \times \text{height} $$
Plugging in the dimensions:
$$ V = 3 \times 3 \times 3 $$
- Perform the multiplication
Calculate the product step by step:
First, calculate ( 3 \times 3 = 9 ).
Next, multiply this result by 3:
$$ 9 \times 3 = 27 $$
- State the final volume
The volume of the rectangular prism filled with 1 by 1 unit cubes is 27 cubic units.
The volume of the rectangular prism is ( 27 ) cubic units.
More Information
A rectangular prism's volume is calculated by multiplying its dimensions (length, width, and height). In this case, the prism was a cube with dimensions 3 units in each direction, leading to a total volume of 27 cubic units, indicating that it can hold 27 unit cubes.
Tips
- Not multiplying all three dimensions, which can lead to an incorrect volume.
- Miscounting the number of units in each dimension, which can skew the final result.
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