Math, asked by gdisha90, 1 month ago

Three circles of radius 1 touch each other externally as shown. The shaded area of the gap as shown
is equal to:​

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Answers

Answered by rambabu083155
0

Answer:

\frac{7\sqrt{3}-11 }{7}cm²

Step-by-step explanation:

As we know that area of shaded region= Area of equilateral triangle of side 2cm- 3* area of sector of having radius 1 cm and 60°

=> \frac{\sqrt{3} }{4}a^{2}- 3*\frac{60 }{360}  \pi r^{2}

here, a=2cm and r= 1 cm

=> \frac{\sqrt{3} }{4}2^{2} - \frac{180}{360}*\frac{22}{7} *1

=> \frac{7\sqrt{3}-11 }{7} cm^{2}

#SPJ3

Answered by Syamkumarr
0

Answer:

The answer is \frac{ [7\sqrt{3} - (11)]}{7} units

Step-by-step explanation:

Given data radius of the circles r = 1 unit

If join the centers of the 3 circles an equilateral triangle will be formed

then each side of the triangle = 1+1 = 2 units

And the area of the shaded part = Area of the triangle - 3( area sector)  

Now we will find area of the equilateral triangle and area of the sector

Area of the equilateral triangle

As we know area of equilateral triangle = \frac{\sqrt{3} }{4} a^{2}  

where a is side of the triangle  

Therefore, area of the triangle =\frac{\sqrt{3} }{4} (2)^{2} = \frac{\sqrt{3} }{4} (4) = \sqrt{3} units  

Area of the sector

Area of the sector = (θ/360°) × πr²,      

Where θ is angle of sector which is formed at center  

As we know angle in a equilateral triangle is equals to 60°  

⇒ angle of sector θ = 60°  

Area of the sector = \frac{60}{360} (\pi )(1^{2} ) =  \frac{1}{6} (\frac{22}{7} ) = (\frac{11}{21} ) units

Area of the shaded part = \sqrt{3} - 3(\frac{11}{21} )

                                         =  \frac{21\sqrt{3} -3 (11)}{21}

                                         = \frac{3[7\sqrt{3} - 11]}{21}

                                         = \frac{ [7\sqrt{3} - 11]}{7} units

#SPJ3

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