Find the area of the unshaded portion of the given figure within the rectangle.

Given,

Radius of circle = 3 cm.

From figure,

Length of rectangle = Diameter of first circle + Diameter of second circle + Radius of third circle

= 6 + 6 + 3

= 15 cm.

Breadth of rectangle = Diameter of a circle = 6 cm.

Area of rectangle = length × bredath

= 15 × 6 = 90 cm².

Area of 2 full circles = 2 × πr²

= 2 × 3.14 × 3²

= 6.28 × 9

= 56.52 cm².

Area of 1 semicircle = $\dfrac{1}{2}$ × πr²

= $\dfrac{1}{2}$ × 3.14 × 9 = 14.13 cm².

From figure,

Area of unshaded portion = Area of rectangle - Area of 2 full circle - Area of semicircle

= 90 - 56.52 - 14.

= 90 - 70.65

= 19.35 cm².

Hence area of unshaded region = 19.35 cm².