A rectangular box with an open top is constructed from cardboard to have a square base of area `x^(2)` and height h. If the volume of this box is 50 cubic units, how many square units of cardboard in terms of x, are needed to build this box ?

Options

A. `5x^(2)`
B. `6x^(2)`
C. `(200)/(x)+x^(2)`
D. `(200)/(x)+2x^(2)`

Answer

C

Explanation

Use the given volume = 50 to get h in terms of x :
Volume = length `xx` width `xx` height
`50 = x.x.h`
`h=(50)/(x^(2))`
The area you're looking for is equal to four lateral faces and one bottom face.
Each lateral face has are `xh=x(50)/(x^(2))=(50)/(x)`, and the base has area `x^(2)`, so the total area you're looking for is
`4((50)/(x))+x^(2)=(200)/(x)+x^(2)`