Question

gabriela builds a rectangular prism that has a volume of 36 cubic units. each rectangular prism below is built with unit cubes. which rectangular prisms could be gabrielas prism? choose all the correct answers.

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular prism is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height. We need to find combinations of $l$, $w$ and $h$ such that $l\times w\times h=36$.

Step2: Factorize 36

The factor - pairs of 36 are: $36 = 1\times1\times36$, $36 = 1\times2\times18$, $36 = 1\times3\times12$, $36 = 1\times4\times9$, $36 = 1\times6\times6$, $36 = 2\times2\times9$, $36 = 2\times3\times6$, $36 = 3\times3\times4$.

Step3: Analyze the prisms

Count the number of unit - cubes along length, width and height for each given rectangular prism and calculate the volume using $V = l\times w\times h$.

Answer:

We need to count the number of unit - cubes along the length, width and height of each prism in the image and calculate their volumes. Without the actual counts from the image (since we can't directly count from a text - based input), if we assume we have counted and found the volumes of the prisms: A prism with dimensions $l = 3$, $w = 3$, $h = 4$ has a volume $V=3\times3\times4 = 36$ cubic units. We would check each prism in the image by counting the unit - cubes along each edge and applying the volume formula $V = l\times w\times h$ to determine which ones have a volume of 36 cubic units.