Question

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, determine how many square units of cardboard are required to make this box ( in terms of $x$ ).

• A. $5x^2$
• B. $6x^2$
• C. $\frac{200}{x}+x^2$
• D. $\frac{200}{x}+2x^2$

Answer 1

Answer: (C)

$\frac{200}{x}+x^2$

Volume is $50=h{x}^2$ $\Rightarrow h=\frac{50}{x^2}$
Area of base is $x^2$.
Area of rectangular faces is $x\times h=\frac{50}{x}$
There are $4$ rectangular faces and $1$ base in our cardboard box $($ top open $)$.
So, the total surface area is $x^2+4\times \frac{50}{x}=\frac{200}{x}+x^2$.