Question

From a square sheet perimeter 112 centimetre circle of maximum area is cut out find the circumference of the circle cut out also find the area of the sheet left

Answer 1

Answer:

circumference = 88 cm^2 and area left= 168 cm^2

Answer 2

Circumference of the circle = 88cm

Area of the remaining sheet = 168cm²

Given that the perimeter of the of the square = 112 cm

Perimeter of the square = 4a = 112

=> a= 28cm

For the circle cut from the square sheet to be of maximum area , the diameter of the circle will be equal to the side of the square sheet.

=> 2r = a

=> r= 14cm

Circumference = 2πr = 88 cm

Area of the sheet remaining after cutting the circle = area of square sheet - area of the circle

=> a² - πr²

=> (28)² - π(14)²

=> 784 - 616

=> 168 cm²