Question

geeta has 240 cubic inches of sand. she is filling rectangular-prism containers that are 4 inches by 4 inches by 2 inches geeta uses the sand to completly fill as many containers as she can how much more sand does geeta need to completly fill the final container enter the answer below

Answer 1

First, we need to calculate the volume of one rectangular prism container.

The volume \( V \) of a rectangular prism is calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

In this case, the dimensions of the container are 4 inches by 4 inches by 2 inches:

\[
V = 4 \, \text{inches} \times 4 \, \text{inches} \times 2 \, \text{inches} = 32 \, \text{cubic inches}
\]

Next, we need to determine how many of these containers Geeta can completely fill with her 240 cubic inches of sand:

\[
\text{Number of containers} = \frac{\text{Total volume of sand}}{\text{Volume of one container}} = \frac{240 \, \text{cubic inches}}{32 \, \text{cubic inches}} = 7.5
\]

Since Geeta can only fill whole containers, she can fill 7 containers completely. Now we calculate the total volume of sand used to fill 7 containers:

\[
\text{Volume used} = 7 \, \text{containers} \times 32 \, \text{cubic inches/container} = 224 \, \text{cubic inches}
\]

Now we find out the remaining sand after filling 7 containers:

\[
\text{Sand remaining} = 240 \, \text{cubic inches} - 224 \, \text{cubic inches} = 16 \, \text{cubic inches}
\]

Now, we know that Geeta needs to completely fill one more container, which has a volume of 32 cubic inches. The amount of sand needed to completely fill the final container is:

\[
\text{Sand needed} = 32 \, \text{cubic inches} - 16 \, \text{cubic inches} = 16 \, \text{cubic inches}
\]

Therefore, Geeta needs **16 cubic inches** more sand to completely fill the final container.