Question

In the given figure, find the area of the unshaded portion within the rectangle (Take π = 3.14).

Answer 1

From the figure:

Radius of each circle = 3 cm

There are three equal circles placed side by side inside the rectangle.

π = 3.14

Step 1: Dimensions of the rectangle

Each circle has:

Diameter

= 2 × 3 

= 6 cm

Since three circles are placed side-by-side:

Length of rectangle

= 3 × 6 

= 18 cm

Height of rectangle = Diameter

= 6 cm

Area of rectangle

= 18 × 6 

= 108 cm²

Step 2: Area of three circles

Area of one circle:

πr² = 3.14 × 3²

= 3.14 × 9

= 28.26 cm²

Area of three circles:

3 × 28.26

= 84.78 cm²

Step 3: Unshaded portion inside the rectangle

Unshaded area = Area of rectnagle – Area of circles

= 108 – 84.78

= 23.22 cm²

However, from the diagram, the two end semicircular parts outside the rectangle are shaded, so only the middle full circle lies completely inside the rectangle.

Thus, area of circles inside the rectangle:

Area = Area of middle circle + Two semicircles

Two semicircles = 1 full circle.

So, total area inside rectangle = 2 circles

2 × 28.26 = 56.52

Now, Unshaded area = 108 – 56.52

= 19.35 cm²