Three circles of radius 1 touch each other externally as shown. The shaded area of the gap as shown
is equal to:
Answers
Answer:
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°
=>
here, a=2cm and r= 1 cm
=>
=>
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Answer:
The answer is 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 =
where is side of the triangle
Therefore, area of the triangle = = = 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 = = = units
Area of the shaded part =
=
=
= units
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