What is the maximum area that can be covered by three non-intersecting circles drawn inside a rectangle of sides 8 cm and 12 cm? 

Formula used:

Area of circle = πr²

Calculation:

To achieve the maximum coverage, we will arrange the circles such that the

larger circle (with a radius of 4 cm) is inscribed within the rectangle, and the

two smaller circles (each with a radius of 2 cm) are positioned at opposite

corners of the rectangle.

As shown in the figure, radius of three circle will be 4 cm, 2 cm, 2 cm.

Therefore, total area

⇒ 16π cm² + 8π cm²

⇒  24π cm²

∴ Required area is 24π cm².