6 circles with radius 7 cm is drawn in such a way that their centres xx the vertices of a regular hexagon. Another circle with radius 7 CM is drawn touching all circles externally. Find the area of the shaded part
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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 centres 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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