A rectanglular box with a cover is to have a square base. The volume is to be 10 cubic cm The surface area of the box in terms of the side x is given by which one of the following functions ?

Options

A. `f(x)=(40/x)+2x^(2)`
B. `f(x)=(40/x)+x^(2)`
C. `f(x)=(40/x)+x`
D. `f(x)=(60/x)+2x`

Answer

A

Explanation

Let the height of rectangular box be y cm
`therefore` volume `=x xx xx y`
`rarr y =(10)/(x^(2))`
Now surface area of box
`=2(x^(2)+xy+yx)=2(x^(2)+2xy)`
`=2x^(2)+(40)/(x)`