Question

4 john builds a rectangular prism that has a volume of 12 cubic units. each rectangular prism below is built with unit cubes. which rectangular prisms could be johns prism? choose all the correct answers.

Explanation:

Step1: Recall volume formula for rectangular prism

The volume $V$ of a rectangular prism made of unit - cubes is found by multiplying the length $l$, width $w$, and height $h$, i.e., $V = l\times w\times h$. Since each cube is a unit cube, we count the number of unit - cubes in each dimension.

Step2: Analyze Option A

In Option A, assume the length $l = 4$, width $w = 2$, and height $h = 1$. Then $V=l\times w\times h=4\times2\times1 = 8$ cubic units.

Step3: Analyze Option B

In Option B, assume the length $l = 4$, width $w = 2$, and height $h = 1$. Then $V = l\times w\times h=4\times2\times1=8$ cubic units.

Step4: Analyze Option C

In Option C, assume the length $l = 6$, width $w = 1$, and height $h = 2$. Then $V=l\times w\times h=6\times1\times2 = 12$ cubic units.

Step5: Analyze Option D

In Option D, assume the length $l = 3$, width $w = 2$, and height $h = 2$. Then $V=l\times w\times h=3\times2\times2=12$ cubic units.

Step6: Analyze Option E

In Option E, assume the length $l = 6$, width $w = 2$, and height $h = 2$. Then $V=l\times w\times h=6\times2\times2 = 24$ cubic units.

Answer:

C. Option C, D. Option D