Question

The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumference of the circles.

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

Answer 1

Let the radii of the two circles be r₁ cm and r₂ cm.

Now, Sum of the radii of the two circles = 7 cm

r₁ + r₂ = 7   ...(i)

Difference of the circumferences of the two circles = 88 cm

⇒ 2πr₁ – 2πr₂ = 8

⇒ 2π(r₁ – r₂) = 8

= `(r_1 - r_2) = 8/(2π)`

⇒ `r_1 - r_2 = (8)/(2 xx 22/7)`

⇒ `r_1 - r_2 = (8 xx 7)/44`

`r_1 - r_2 = 56/44`

`r_1 - r_2 = 14/11`   ...(ii)

Adding (i) and (ii), we get

`2r_1 = 91/11`

`r_1 = 91/22`

∴ Circumference of the first circle = 2πr₁

= `2 xx 22/7 xx 91/22`

= 26 cm

Also,

`r_1 - r_2 = 14/11`

`91/22 - r^2 = 14/11` 

`91/22 - 14/11 = r_2`

`r_2 = 63/22`

∴ Circumference of the second circle = 2πr₂

`= 2 xx 22/7 xx 63/22`

= 18 cm

Therefore, circumferences of the first and second circles are 18 cm and 26 cm, respectively.