Question

1. add a layer to box d and compare the volume of the new box d to the volume of box e. 6. 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.

Explanation:

Step1: Count unit - cubes in Box D

Count the number of unit - cubes in Box D before adding a layer. Assume the length is $l_D$, width is $w_D$ and height is $h_D$. The volume of Box D, $V_D=l_D\times w_D\times h_D$. Let's assume from the figure, $l_D = 5$, $w_D=3$, $h_D = 1$, so $V_D=5\times3\times1 = 15$ unit - cubes. After adding a layer (assuming the new height $h_{D_{new}}=2$), the new volume $V_{D_{new}}=5\times3\times2=30$ unit - cubes.

Step2: Count unit - cubes in Box E

Count the number of unit - cubes in Box E. Assume the length is $l_E$, width is $w_E$ and height is $h_E$. From the figure, $l_E = 4$, $w_E = 3$, $h_E=3$. Then the volume of Box E, $V_E=l_E\times w_E\times h_E=4\times3\times3 = 36$ unit - cubes.

Step3: Compare volumes

Compare $V_{D_{new}}$ and $V_E$. Since $30<36$, Box E has a greater volume.

Answer:

Box E has a greater volume. Because the volume of Box D after adding a layer is 30 unit - cubes and the volume of Box E is 36 unit - cubes.