To determine the height of a rectangular solid given its volume, length, and width, we can use the formula for the volume of a rectangular solid:
[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.
We know from the problem:
- The volume [tex]\( V \)[/tex] is 240 cubic feet,
- The length [tex]\( l \)[/tex] is 6 feet,
- The width [tex]\( w \)[/tex] is 8 feet.
We want to find the height [tex]\( h \)[/tex]. To do this, we can rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{V}{l \times w} \][/tex]
Now, substitute the known values into this equation:
[tex]\[ h = \frac{240}{6 \times 8} \][/tex]
[tex]\[ h = \frac{240}{48} \][/tex]
[tex]\[ h = 5 \text{ feet} \][/tex]
Thus, the height of the rectangular solid is 5 feet.
