Question

A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in. squares from each corner and folding up the sides. The box is to hold 2527 in3. How big a piece of cardboard is needed?

Answer 1

Answer:

The size of the cardboard should be  $26 in\ by\ 26in$

Step-by-step explanation:

The diagram for this question is shown on the first uploaded image

     The volume of the box is  $V = 2527 \ in ^3$

The length and the Width of the card is  

      L = W = Z

From the question we are told that 7 in squares were cut from each corner

So the length and the width of the box  would be  

              L = W = (Z - 7)

And the height would be  H  =  7 in

Mathematically the volume of the box can be represented as

              $V = Length\ of\ bx * Width\ of\ box * Height\ of\ box$

So the Volume would be

         $V = (Z-7)(Z-7) * 7$

Substituting values

         $(Z-7) ^2 = \frac{2527}{7}$

          $(Z-7) ^2 = 361$  

          $(Z-7) ^2 = 19^2$

=>   $Z - 7 = 19$

        $Z = 19 + 7$

         $Z =26 \ in$