Question

on a square handkerchief nine circular design each of radius 7 cm are made find the area of the remaining portion of the handkerchief​

Answer 1

Solution:

Given:

=> Radius of circle = 7 cm.

=> Diameter of circle = 7 × 2 cm

                                  = 14 cm.

=> Side of square ABCD = 3 × 14 = 42 cm.

To find:

=> Area of remaining portion.

Formula used:

$\sf{\implies Area\;of\;square=(side)^{2}}$

$\sf{\implies Area\;of\;circle = \pi r^{2}}$

So,

$\sf{\implies Area\;of\;square(ABCD)=(side)^{2}}$

$\sf{\implies 42\times 42}$

$\sf{\implies 1764\;cm^{2}}$

$\sf{Now,\;Area\;of\;circle=\pi r^{2}}$

$\sf{\implies \dfrac{22}{7}\times 7\times 7}$

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

There are 9 circles on handkerchief.

So, Area of 9 circles = 154 × 9 = 1386 cm²

Now, Area remaining portion = Area of square(ABCD) - Area of 9 circles.

=> 1764 - 1386

=> 378 cm²

Answer 2

Answer:

378 cm ^2

Step-by-step explanation:

Radius of the circle = 7 cm

• area of the remaining portion of the handkerchief = area of square - area of 9 circles

• area of square = (side)^2

side = 3 × diameter

radius = 7 cm

diameter = 7 × 2 = 14 cm

side of the square = 3 × 14 = 42 cm

area of square = (42)^2 = 1764 cm^2

• area of circle = πr^2

22/7 × 7 × 7= 154 cm^2

area of 9 circles = 154 cm^2 × 9 = 1386 cm^2

Area of remaining part of the kerchief =

                            1764 - 1386 = 378 cm^2

                   area of remaining part of the kerchief = 378 cm^2