Absolutely, let's walk through this step by step to solve the problem.
### Step 1: Understand the dimensions of the sandbox
- The sandbox has a base that is a square with a side length of 5 feet.
- The height (or depth) of the sandbox is 8 inches.
### Step 2: Convert the height into the same units
Since the side length is in feet, we should convert the height from inches to feet to ensure consistent units.
There are 12 inches in a foot, so:
[tex]\[ \text{Height in feet} = \frac{8 \text{ inches}}{12 \text{ inches/foot}} = \frac{2}{3} \text{ feet} \approx 0.6667 \text{ feet} \][/tex]
### Step 3: Calculate the volume of the sandbox
The volume [tex]\( V \)[/tex] of a rectangular prism (in this case, the sandbox) is given by the product of its length, width, and height.
The side length of the sandbox (length and width) is 5 feet, and the height is [tex]\( \frac{2}{3} \)[/tex] feet. So the volume can be calculated by:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]
[tex]\[ V = 5 \text{ feet} \times 5 \text{ feet} \times \frac{2}{3} \text{ feet} \][/tex]
[tex]\[ V = 25 \text{ square feet} \times \frac{2}{3} \text{ feet} \][/tex]
[tex]\[ V = \frac{50}{3} \text{ cubic feet} \][/tex]
We can simplify this division to get a decimal approximation:
[tex]\[ V \approx 16.6667 \text{ cubic feet} \][/tex]
### Step 4: Determine the amount of sand left over
You bought 20 cubic feet of sand. To find out how much sand is left over, we subtract the volume of the sandbox from the total amount of sand purchased.
[tex]\[ \text{Sand left over} = \text{Total sand} - \text{Volume of the sandbox} \][/tex]
[tex]\[ \text{Sand left over} = 20 \text{ cubic feet} - 16.6667 \text{ cubic feet} \][/tex]
[tex]\[ \text{Sand left over} \approx 3.3333 \text{ cubic feet} \][/tex]
### Conclusion
You will have approximately 3.33 cubic feet of sand left over after filling the sandbox to the top.
