Question

On a square handkerchief, nine circular designs each of radius 7 cm are made. Find the area of the remaining portion of the handkerchief.

Answer 1

Given :-

Number of circular designs = 9

Radius of the circular design = 7 cm

To Find :-

The area of the remaining portion of the handkerchief.

Solution :-

We know that,

• r = Radius
• d = Diameter
• a = Area

Given that,

Number of circular designs = 9

Radius of the circular design (r) = 7 cm

There are three circles in one side of square handkerchief.

According to the question,

Diameter = 2 × radius

Diameter = 2 × 7 = 14 cm

Side of the square = 3 × Diameter of circle

Substituting them,

3 × 14 = 42 cm

By the formula,

$\underline{\boxed{\sf Area \ of \ square=Side \times Side}}$

Substituting their values,

Area of the square = = 1764 cm²

$\underline{\boxed{\sf Area \ of \ circle= \pi r^{2}}}$

Substituting them,

$\sf \dfrac{22}{7} \times 7 \times 7=154 \ cm^{2}$

Therefore, area of the circle is 154 cm²

Total area of the design = Number of circular designs × Area of the circle

By substituting,

Total area of the design = 9 × 154 = 1386 cm²

Area of the remaining portion of the handkerchief = Area of the square – Total area of the design

Substituting them,

Area of the remaining portion of the handkerchief = 1764 – 1386 = 378 cm²

Therefore, 378 cm² is remaining.