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 the original Box D. Assume the original number of unit - cubes in Box D is $n_D$.

Step2: Add a layer

When a layer is added to Box D, count the number of unit - cubes in the new layer. Let the number of unit - cubes in the new layer be $m$. The new number of unit - cubes in Box D is $n_{D_{new}}=n_D + m$.

Step3: Count unit - cubes in Box E

Count the number of unit - cubes in Box E, say $n_E$.

Step4: Compare volumes

Compare $n_{D_{new}}$ and $n_E$. If $n_{D_{new}}>n_E$, then the volume of the new Box D is greater; if $n_{D_{new}}

For the second part:

Step1: Count unit - cubes in Box D and Box E

Count the number of unit - cubes in Box D, say $n_D$, and in Box E, say $n_E$.

Step2: Compare and explain

If $n_D>n_E$, then Box D has a greater volume because volume is determined by the number of unit - cubes it contains. If $n_D < n_E$, then Box E has a greater volume for the same reason. If $n_D=n_E$, then they have equal volumes as they contain the same number of unit - cubes.

Since we don't have the actual counts of unit - cubes from the picture, we can't give a numerical answer. But the general method is as above.

Answer:

We need to count the number of unit - cubes in each box (original Box D, new Box D after adding a layer, and Box E) to compare their volumes. For the question of which has a greater volume between Box D and Box E, count the unit - cubes in each and compare. If Box D has more unit - cubes, its volume is greater; if Box E has more unit - cubes, its volume is greater; if they have the same number of unit - cubes, their volumes are equal.