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A square piece of card has a square of side 2 cm cut out from
each of its corners. The remaining card is then folded along
the dotted lines shown to form an open box whose total
internal surface area is 180 cm².
What is the volume of the open box in cm³?
A 100 B 128 C 162 D 180 E 200

A square piece of card has a square of side 2 cm cut out from each of its corners The remaining card is then folded along the dotted lines shown to form an open class=

Respuesta :

devishri1977

Answer:

E) 200

Step-by-step explanation:

Let the length of the side after cutting the corners =x cm

Length of the side before cutting the corners = x + 4 cm

Area of square before cutting =  (x + 4)² square cm

Area of that square that was cut  = 2*2 = 4 cm²

Area of 4 squares cut from all 4 corners = 4 * 4 = 16 cm²

Area of internal surface area = 180 square cm

                       (x + 4)² -  4*4        = 180

                   x² + 2*4*x + 4² - 16 = 180

 {expand using the identity  (a + b)² = a² + 2ab + b²) }

                     x²  + 8x + 16 -16   = 180

                        x² + 8x  - 180    = 0

                  x² + 18x - 10x - 180 = 0

               x( x + 18) - 10(x + 18) = 0

                         (x + 18) (x - 10) = 0

  x - 10 = 0   {Ignore x +18 = 0}

         x = 10

Open box:

           length =  x = 10 cm

          breadth = x = 10 cm

         height  = 2 cm

Volume of open box = length * breadth * height

                                  = 10 * 10 * 2

                                  = 200 cm³

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