Multiple choice

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 $x$ ).

  1. $5x^{2}$
  2. $6x^{2}$
  3. $\dfrac {200}{x} + x^{2}$
  4. $\dfrac {200}{x} + 2x^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume V = x^2 * h = 50, so h = 50/x^2. The surface area of an open-top box with a square base is the base area (x^2) plus four side faces (4 * x * h). Substituting h, we get x^2 + 4 * x * (50/x^2) = x^2 + 200/x.

AI explanation

The volume of the box equals the base area times the height, so 50 equals x squared times h, meaning h is 50 divided by x. The cardboard needed includes the base area of x squared plus the area of the four sides, which is 4 times x times h. Substituting h yields x squared plus 4 times x times 50 divided by x, resulting in 200 divided by x plus x squared.

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