Question

A sandbox in the shape of a rectangular prism is 2 feet deep. Filled to the top, it holds 72 cubic feet of sand. Select all that could be the dimensions of the base of the sandbox.

Answer 1

To determine the dimensions of the base of the sandbox, we start with the formula for the volume of a rectangular prism:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

In this case, the height (or depth) of the sandbox is given as 2 feet. We know the volume is 72 cubic feet, so we can set the equation as follows:

\[
72 = \text{length} \times \text{width} \times 2
\]

To find the area of the base (length × width), we can simplify this equation:

\[
\text{length} \times \text{width} = \frac{72}{2} = 36
\]

This means that the product of the length and width must equal 36 square feet.

Now, we will look for pairs of numbers (length and width) that multiply to 36. The possible pairs of positive dimensions (length and width) are:

1. \(1 \times 36\)
2. \(2 \times 18\)
3. \(3 \times 12\)
4. \(4 \times 9\)
5. \(6 \times 6\)

Thus, the possible dimensions of the base of the sandbox can be any of the following pairs of length and width:

- Length: 1 ft, Width: 36 ft
- Length: 2 ft, Width: 18 ft
- Length: 3 ft, Width: 12 ft
- Length: 4 ft, Width: 9 ft
- Length: 6 ft, Width: 6 ft

So, any of these pairs of dimensions can be considered as a suitable option for the base of the sandbox.