Question

Question 10
On a cardboard sheet of area $784c{m}^2$, 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.

Answer 1

$\because$ Area of square = 784

$\therefore (side{)}^2=(28{)}^2$

$\Rightarrow$ side = 28 cm

Since, all four are congruent circular plates.

$\therefore$ Diameter of each circular plate = 14 cm

$\therefore$ Radius of each circular plate = 7 cm

Now, area of one circular plate $=\pi r^2=\frac{22}{7}(7{)}^2$

$=154c{m}^2$

$\therefore$ Area of four circular plates $=4\times 154=616c{m}^2$

$\therefore$ Area of the square sheet not covered by the circular plates
= Area of the square - Area of the four circular plates
$=784-616=168c{m}^2$