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  • On a square cardboard sheet of area 784 cm2, four congruent circular plates of Maximum size are placed such that each circular plate touches the other two Plates and each side of the square sheet is tangent to two circular plates. Find The area of the squ

On a square cardboard sheet of area 784 cm2, four congruent circular plates of Maximum size are placed such that each circular plate touches the other two Plates and each side of the square sheet is tangent to two circular plates. Find The area of the square sheet not covered by the circular plates.

Answers (1)

[168 cm2]

Solution

            

Given area of sheet =784 cm2

Let the side of the sheet = a

a2=7842                                        (Area of square = (side) 2)

a=\sqrt{784}=28cm

Diameter of each circular plate =\frac{a}{2}=\frac{28}{2}=14cm

 Radius =\frac{d}{2}=\frac{14}{2}=7cm

Area of 4 circular plates =4 \times \pi r^{2}

                                      \\=4 \times \frac{22}{7} \times 7 \times 7\\ =616cm^{2}

Area of sheet not covered with circular plates = Area of sheet – Area of 4 circular plates.

                                                                        =784-616=168cm2

           

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