From a square cardboard, a circle of biggest area was cut out. If the area of the circle is 154 cm², calculate the original area of the cardboard.

Let radius of the circle be r cm.

Given,

Area of the circle = 154 cm²

πr² = 154

$\Rightarrow \dfrac{22}{7} \times r^2 = 154 \\[1em] \Rightarrow r^2 = \dfrac{154 \times 7}{22} \\[1em] \Rightarrow r^2 = 49 \\[1em] \Rightarrow r = \sqrt{49} = 7 \text{ cm}.$

The biggest circle that can be cut from a square has the diameter equal to the side of the square.

Side = 2r = 2 × 7 = 14 cm.

Area of cardboard = (side)² = 14² = 196 cm².

Hence, area of cardboard = 196 cm².