Question

From a square card board of size 21cm,a circle of maximum area is cut out. Find the area of cardboard left.
[Hint Diameter of circle of maximum area = 21cm]

Answer 1

Dear Student,
Solution)
When a circle of maximum area is cut out from a square board, then the diameter of the circle will be equal to the side of square.
So, diameter of circle = 21 cm
Then, its radius = 10.5 cm
So, area of circle = ${\mathrm{\pi r}}^2=\frac{22}{7}\times {\left(10.5\right)}^2=346.5{\mathrm{cm}}^2$
And area of square = ${\left(21\right)}^2=441{\mathrm{cm}}^2$
Therefore,
Remaining area = area of square - area of circle
= $441{\mathrm{cm}}^2-346.5{\mathrm{cm}}^2=94.5{\mathrm{cm}}^2$
Regards!