Let's walk through the math problems on the sheet.

Question 4:

The problem asks how many small boxes fit in the large container. The large container dimensions are 16 inches (high) × 10 inches (wide) × 4 inches (deep), and the small box dimensions are 1 inch (high) × 1 inch (wide) × 1 inch (deep).

To find how many boxes fit, you need to divide the volume of the large container by the volume of a small box:

• Volume of the large container: $16 \times 10 \times 4 = 640 \, \text{cubic inches}$
• Volume of a small box: $1 \times 1 \times 1 = 1 \, \text{cubic inch}$

So, the number of small boxes that fit is: $\frac{640}{1} = 640 \, \text{boxes}$ You correctly noted 64 boxes at first, but then corrected it to 640, which is the right answer.

Question 5:

Since each small box holds 10 gas molecules, the total number of gas molecules in the large container is: $640 \, \text{boxes} \times 10 \, \text{molecules per box} = 6,400 \, \text{molecules}$

Question 6:

The aquarium has a square base with an area of 36 square inches, and it holds a volume of 360 cubic inches. To find the height, use the formula for the volume of a rectangular prism: $\text{Volume} = \text{Base Area} \times \text{Height}$ Given that the base area is 36 and the volume is 360, the height $h$ is: $36 \times h = 360$ $h = \frac{360}{36} = 10 \, \text{inches}$ So the height of the aquarium is 10 inches. Your calculation and answer are correct here as well.

Question 7:

Now the height is changed to 30 inches, and we are asked how much water the tank will hold (assuming the base area remains the same). The new volume is: $\text{Volume} = \text{Base Area} \times \text{New Height} = 36 \times 30 = 1,080 \, \text{cubic inches}$ Your answer of 1,080 cubic inches is correct.

Question 8:

For this one, it asks how you could change the length, width, and height while keeping the same volume. Since the volume is constant at 1,080 cubic inches, you can vary any of the dimensions as long as the product of the base area and height equals 1,080.

For example, if you reduce the base area, you would need to increase the height, or vice versa. Any combination of dimensions that satisfies this product would work.

Would you like more detailed explanations on any of these problems? Here are some related questions you might find useful:

1. How do you calculate the volume of irregularly shaped objects?
2. What are some real-world examples where volume calculations are essential?
3. How does the formula for volume differ for other shapes like cylinders or spheres?
4. Can you explain the relationship between surface area and volume in 3D objects?
5. How does scaling dimensions of an object affect its volume?

Tip: Always double-check units when calculating area, volume, and other measurements to avoid mistakes!