Question

19. On a square handkerchief, 9 circular
designs each of radius 7 cm are made (see
the figure). Find the area of the remaining
portion of the handkerchief​

Answer 1

• The area of the remaining portion(having no circular design) is 378 cm sq.

Step-by-step explanation:

Given:

• The radius (r) of each circle in the handkerchief is = 7cm

To find:

Area of the remaining portion

So,

Diameter = 2 * radius

Diameter = 2 * 7 = 14 cm

[From the figure we can conclude that the diameter of the three circular designs is the length of the side of the square(i.e. square shape handkerchief.) ]

Thus,

Length of each side of square = 3 * diameter of three circular designs

Length of each side of square = 3 * 14 = 42 cm

• The formula to find the area of the square is = (side)² units sq.

→ The area of the square-shaped handkerchief is = (42)² = 1764 cm sq.

• The formula to find the area of a circle is = πr² units sq.

Therefore, the area of one circular shape design is

→ πr² = 22/7 * (7)²

        = 22 * 7

        = 154 cm sq.

Now,

Area of one circular design = 154 cm sq.

Area of 9 such circular designs = 9 * 154 = 1386 cm sq.

• The area of the remaining portion of the square-shaped handkerchief will be = Area of 9 circular designs

= 1764 - 1386

= 378 cm sq.

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More Information

Square:

• It s quadrilateral which has the same sides.
• The all four interior angles are 90° each.
• The perimeter of square = 4 * side units.
• The diagonal of the square = side√2 units.

Circle:

• The Circumference of the circle = 2πr units.