Question

The sum of radii of two circles is 7cm.difference of their circumference is 8cm.find the circumferences of the circles ​

Answer 1

Answer:

26 cm and 18 cm  where r₁ >  r₂

Step-by-step explanation:

Let the radii be r₁  and  r₂ &  r₁ >  r₂

Given their sum is 7 cm.

i.e.   r₁ + r₂ = 7 ... ( i )

The difference of their circumference = 8 cm

i.e.  2 π r₁ - 2 π r₂ = 8

r₁ -  r₂ = 4 /  π ... ( ii )

From ( i )  and  ( ii )  we get :

2 r₁  = 7 +  4 /  π    [ 22 / 7 =  π ]

r₁ = 91 / 22 cm

For  r₂ :

r₁ + r₂ = 7 ... ( i )

r₂ =  7 - 91 / 22

r₂ = 63 / 22 cm

Now their circumference :

⇒ 2 π r₁  

⇒ 2 × 22 / 7 × 91 / 22

⇒ 2 × 13

⇒ 26 cm

For second circle :

⇒ 2 π r₂

⇒ 2 × 22 / 7 × 63 / 22

⇒ 2 × 9

⇒ 18 cm.

Hence , circumferences of the circles ​are 26 cm and 18 cm.

Answer 2

AnswEr :

• Circumference of 1st Circle = 26 cm
• Circumference of 2nd Circle = 18 cm

Explanation :

Let the Radius of 1st Circle be r₁ and Radius of 2nd Circle be r₂.

• Given :

» r₁ + r₂ = 7cm

» r₁ = 7 – r₂ —(¡)

• Difference of Circumference of Circles :

⇒ Circumference of 1st Circle – Circumference of 2nd Circle = 8cm

⇒ (2 π r₁) – (2 π r₂) = 8

⇒ 2 π ( r₁ – r₂ ) = 8

⇒ ( r₁ – r₂ ) = 8 / 2 π

⇒ ( r₁ – r₂ ) = 4 / π

⇒ 7 – r₂ – r₂ = 4 / π —( from ¡ )

⇒ 7 – 2 r₂ = 4 / π

⇒ 7 – 4 / π = 2 r₂

⇒ 7 – (4 × 7) / 22 = 2 r₂ [ π = 22 / 7 ]

⇒ (154 – 28) / 22 = 2 r₂

⇒ 126 / 22 = 2 r₂

⇒ r₂ = 63 / 22

• Putting value of r₂ in Equation (¡)

⇒ r₁ = 7 – r₂

⇒ r₁ = 7 – 63 / 22

⇒ r₁ = 154 – 63 / 22

⇒ r₁ = 91 / 22

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• Circumference of 1st Circle :

⇒ 2 π r₁

⇒ 2 × 22 / 7 × 91 / 22

⇒ 2 × 1 / 7 × 91

⇒ 2 × 13

⇒ 26 cm

• Circumference of 2nd Circle :

⇒ 2 π r₂

⇒ 2 × 22 / 7 × 63 / 22

⇒ 2 × 1 / 7 × 63

⇒ 2 × 9

⇒ 18 cm

჻ Circumference of 1st and 2nd Circles is 26cm and 18cm respectively.