Q1 of 27 Page 228

A rectangular acrylic sheet is 36 cm by 25 cm. From it, 56 circular buttons, each of diameter 3.5 cm have been cut out. Find the area of the remaining sheet.


The dimensions of rectangular sheet are 36 cm by 25 cm.


The Area of rectangular sheet = 36 × 25 = 900 sq.cm


From this sheet, 56 circular buttons are cut as shown,


Diameter of each circle = 3.5 cm


⇒ radius of each button, r = 1.75 cm


Area of one button = πr2



⇒ Area of each button = 9.625 sq.cm


Total area of buttons cut = area of each button × 56


⇒ Total Area of buttons = 539 sq. cm


Area of remaining sheet (area shaded with blue) = (Area of rectangular sheet) – (total area of buttons)


⇒ Req. area = 900 – 539 = 361 sq.cm


∴ Area of the remaining sheet is 361 sq.cm


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