Question

both figures are filled with unit - cubes of the same size. which rectangular prism has the greater volume, figure a or figure b? show your work.
a
b has the greater volume.

Explanation:

Step1: Count unit - cubes in Figure A

Count the number of unit - cubes in Figure A. Let's assume we count and find there are $n_A$ unit - cubes. For example, if we count carefully and find there are 15 unit - cubes in the bottom layer and 2 unit - cubes in the upper layer, so $n_A=15 + 2=17$.

Step2: Count unit - cubes in Figure B

Count the number of unit - cubes in Figure B. Suppose we find there are $n_B$ unit - cubes. For instance, if there are 10 unit - cubes in the bottom layer and 5 unit - cubes in the upper layer, so $n_B = 10+5=15$.

Step3: Compare volumes

Since the volume of a rectangular prism made up of unit - cubes is equal to the number of unit - cubes it contains, and $n_A>n_B$, Figure A has a greater volume.

Answer:

Figure A