Sure, let's calculate the volume of sand needed to fill the space that is dug out.
The space to be filled is a rectangular prism, and the formula for the volume of a rectangular prism is:
[tex]\[ V = l \times w \times h \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume
- [tex]\( l \)[/tex] is the length
- [tex]\( w \)[/tex] is the width
- [tex]\( h \)[/tex] is the height (or depth in this case)
Given:
- Length ([tex]\( l \)[/tex]) = 8 feet
- Width ([tex]\( w \)[/tex]) = 10 feet
- Depth ([tex]\( h \)[/tex]) = 0.5 feet
Now, substitute the values into the formula:
[tex]\[ V = 8 \, \text{feet} \times 10 \, \text{feet} \times 0.5 \, \text{feet} \][/tex]
First, multiply the length and the width:
[tex]\[ 8 \times 10 = 80 \][/tex]
Next, multiply the result by the depth:
[tex]\[ 80 \times 0.5 = 40 \][/tex]
Therefore, the volume of sand needed to fill this space is:
[tex]\[ 40 \, \text{cubic feet} \][/tex]
So, the correct answer is:
[tex]\[ 40 \, \text{ft}^3 \][/tex]
I hope this helps!
