Question

Logo of a car company is shown in the adjoining figure, which consists of three circles each of

radius 3.5 cm. If the company want to colour in the region enclosed by these circles, then find how

much area is available for colouring(see above right sided figure)? [Use π = 22/7, √3 = 1.732]​

Answer 1

Answer:  2  cm²

Explanation:

• In the attached photo, we can see that by joining centers of three circles, equilateral triangle with side 7 cm will be formed.

• As, Radius of circle is 3.5 cm, then Side of triangle = 3.5+3.5 = 7cm

• Area of Shaded region= Area of Triangle - 3*Segment of Circle

• Area of Equilateral Triangle = $\frac{\sqrt{3} }{4} a^{2}$

                                                        = $\frac{\sqrt{3} }{4} 7^{2}$

                                                        =21.21cm²

• Area of Segment QAP of Circle = $\frac{angle \ substended\ by \ the\ circle}{360}*\pi r^{2}$

                                                               = $\frac{60}{360}*\frac{22}{7} (3.5)^{2}$

                                                               = 6.41 cm²

• Area of Shadde region= (21.21 - 3×6.41)cm²

                                               = (21.21 - 19.21)cm²

                                               = 2 cm²

• Hence,the area of shaded region is 2  cm².

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