Answer: 10 inches
Step-by-step explanation:
Given: The volume of a box = 200 cubic inches
The length of the box = 8 inches
The width of the box= \(2\frac{1}{2}=\frac{5}{2}\) inches
We know that the volume of rectangular prism is given by :-
\(\text{Volume}=length*width*height\)
Let h be the height of the box.
Then, we have
\(200=8\times\frac{5}{2}\times h\\\\\Rightarrow\ h=\frac{200}{4\times5}\\\\\Rightarrow\ h=10\ inches\)
Hence, the height of the box = 10 inches.
