From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in figure). Find the area of the remaining sheet.

It is given in the question that,

Radius of bigger circle = 14 cm

Area of the circle = πr^{2}

∴ Area of bigger circle = × 14 × 14

= 22 × 2 × 14

= 44 × 14

= 616 cm^{2}

Also, it is given that:

Radius of two small circles = 3.5 cm

Area of the circle = πr^{2}

∴ Area of 2 small circles =

= 44 × 0.5 × 3.5

= 22 × 3.5

= 77 cm^{2}

Length of rectangle = 3 cm

Breadth of rectangle = 1 cm

Area of rectangle = Length × Breadth

∴ Area of rectangle = 3 × 1

= 3 cm^{2}

Hence,

Remaining area of sheet = Area of bigger circle – Area of 2 small circles – Area of rectangle

= 616 – 77 – 3

= 616 – 80

= 536 cm^{2}

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