Q. 114.6( 199 Votes )

# On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Answer :

Radius of circle is 7 cm.

Diameter of the circle is 14 cm.

As 3 circles are there on one side of the square.

The side of the square will be 14 × 3 = 42 cm

Area of square = (Side)^{2}

= (42)^{2}

= 1764 cm^{2}

Area of each circle = π*r*^{2}

= × (7)^{2}

= 154 cm^{2}

Area of 9 circles = 9 × 154

= 1386 cm^{2}

Area of the remaining portion of the handkerchief = 1764 - 1386

**= 378 cm ^{2}**

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PREVIOUSThe area of an equilateral triangle ABC is 17320.5cm2. With each vertex of the triangle as centre, acircle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region. (Use π = 3.14 and= 1.73205)NEXTIn Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the(i) Quadrant OACB(ii) Shaded region.

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