Question

box d and box e are made from unit - cubes of the same size. which has a greater volume, box d or box e? explain. add a layer to box d and compare the volume of the new box d to the volume of box e.

Explanation:

Step1: Count unit - cubes in Box D

Box D has 3 rows, 3 columns and 5 layers. The volume $V_D$ is calculated by multiplying the number of rows, columns and layers. So $V_D=3\times3\times5 = 45$ unit - cubes.

Step2: Count unit - cubes in Box E

Box E has 4 rows, 4 columns and 2 layers. The volume $V_E$ is calculated by multiplying the number of rows, columns and layers. So $V_E=4\times4\times2=32$ unit - cubes.

Step3: Compare volumes

Since $45>32$, Box D has a greater volume.

Answer:

Box D has a greater volume.

For the second - part:

Step1: Add a layer to Box D

After adding a layer to Box D, the new number of layers is $5 + 1=6$. The new volume $V_{D_{new}}$ of Box D is $V_{D_{new}}=3\times3\times6=54$ unit - cubes.

Step2: Compare new volume of Box D with volume of Box E

Since $54>32$, the new Box D has a greater volume than Box E.