Question

.
6 circles each with radius
7 cm is drawn in such
a way that their centres
form the vertices of a
regular hexagon. Another
circle with radius 7 cm is
drawn touching all the
circles externally. Find
the area of the shaded
part.
(Use #
13 - 1.73)​

Answer 1

Area of the shaded part =  147 (2√3 - π )   = 47.04 cm²

Step-by-step explanation:

6 circles with radius 7 cm is drawn in such a way that their centers at the vertices of a regular hexagon

Side of Regular Hexagon = 2 * 7 = 14 cm

Area of Hexagon = 3√3 (side)²/2

= 3√3*  14²/2

= 294√3  cm²

Area of Hexagon covered by circles :

6 Circles Covering 120° Sector   & 1 Complete Circle

= 6 (120°/360°)π(7)²  + π(7)²

= 2π(7)²  + π(7)²

= 3π(49)

= 147π cm²

area of the shaded part = 294√3 -  147π

= 147 (2√3 - π )  

= 147 ( 3.46 - 3.14)

= 147 ( 0.32)

= 47.04 cm²

area of the shaded part =  147 (2√3 - π )   = 47.04 cm²

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