Harriet needs to ship a small vase. The box she will use has a volume of 216 cubic inches. If the side lengths are all the same, what is the length of each side of the box? Hint: V = \(s^{3}\)
The box has a shape of cube. The volume of cube with side s in is
\(V_{cube}=s^3\ in^2.\)
Since Harriet uses a box of volume 216 cubic inches, then
\(V_{cube}=216\ in^3\)
and, therefore,
\(216=s^3.\)
Note that \(216=6^3,\) then
\(6^3=s^3,\\ \\s=6\ in.\)
Answer: the length of each side of the box is 6 inches.