Question

Three circles are placed on a plane in such a way that each circle just touches the other two , each having a radius of 10cm. Find the area of region enclosed by them.​

Answer 1

Step-by-step explanation:

⇒ Here, AB=BC=AC=10+10=20cm

∴ △ABC is equilateral triangle.

∴ ∠A=∠B=∠C=60

o

⇒ Let a=20cm

⇒ Area of equilateral △ABC=

4

3

×a

2

⇒ Area of equilateral △ABC=

4

3

×(20)

2

∴ Area of equilateral △ABC=

4

400×

3

=173.20cm

2

⇒ Here, θ=60

o

and r=10cm

⇒ Area of 3 sectors =3×

360

o

θ

πr

2

⇒ Area of 3 sectors =3×

360

o

60

o

×

7

22

×(10)

2

∴ Area of 3 sectors =3×52.38=157.14cm

2

⇒ Required area = Area of equilateral triangle - Area of 3 sectors.

⇒ Required area =173.20−157.14=16.06cm

2

Answer 2

Step-by-step explanation:

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⇒ Here, AB=BC=AC=10+10=20cm

∴ △ABC is equilateral triangle.

∴ ∠A=∠B=∠C=60°

⇒ Let a=20cm

⇒ Area of equilateral △ABC = √3/4 × a²

⇒ Area of equilateral △ABC = √3/4 × (20)²

⇒ Area of equilateral △ABC = 400 × √3 / 4

⇒ Area of equilateral △ABC = 173.20 cm²

⇒ Here, θ=60° and r =10cm

⇒ Area of 3 sectors =3× θ/360° × πr²

⇒ Area of 3 sectors =3× 60°/360° ×22/7 × (10)²

∴ Area of 3 sectors =3×52.38=157.14 cm²

⇒ Required area = Area of equilateral triangle - Area of 3 sectors.

⇒ Required area =173.20−157.14=16.06 cm²