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Answer:

remaining cardboard area =  122.5πr²

Step-by-step explanation:

area of original rectangle = length * width                                                                      

                                          =  18r * 8r

                                           =     144r²

  • area of semi circle: [tex]\frac{1}{2}[/tex]πr²

Here we have 3 semi circles with radius 3r:

  • area of 3 semi circles:  3( [tex]\frac{1}{2}[/tex] * π * (3r)²)

                                   : 3( [tex]\frac{1}{2}[/tex] * π * 9r²)

                                    : 13.5πr²

  • area of one semi circle with radius 4r:

                       ( [tex]\frac{1}{2}[/tex] * π * (4r)²)

                       ( [tex]\frac{1}{2}[/tex] * π * 16r²)

                             8πr²

  • So the area of remaining cardboard:

            area of rectangle - area of 4 semi circles

                        144r² - 13.5πr² - 8πr²

                                122.5πr²

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