Step 1Find the volume of the rectangular prism.Substitute \(l=11\) and \(w=8\) into the formula for the volume of a rectangular prism.\(V=lwh\)\(V=11\cdot 8\cdot h\)
Step 2Find the height of the vase.Since the vase is \(\frac{2}{3}\) full, there is \(\frac{2}{3}V\) of water in the vase.Equate the volume of water in the vase to \(\frac{2}{3}V\).\(\frac{2}{3}V=704\)Substitute \(V=11\cdot 8\cdot h\) into the equation.\(\frac{2}{3}V=704\)\(\frac{2}{3}(11\cdot 8\cdot h)=704\)Multiply the numbers in the parentheses.\(\frac{2}{3}\cdot 88h=704\)Calculate the product.\(\frac{176}{3}h=704\)Multiply both sides of the equation by \(\frac{3}{176}\).\(h=12\)SolutionThe height of the vase is \(12\) inches.
