Question

The sum of the radii of two circles is 140 cm and the difference of their circumferences in 88 cm. Find the diameters of the circles.

Answer 1

Let radius of circles be 𝑟₁𝑎𝑛𝑑 𝑟₂

Given sum of radius = 140cm

𝑟₁ + 𝑟₂ = 140 …..(i)

difference in circumferences = 88 𝑐𝑚

2 × 𝑟₁ − 2𝜋𝑟₂ = 88

${\displaystyle 2\times \frac{22}{7}(r_1-r_2)88}$

${\displaystyle r_1-r_2=\frac{88\times 7}{2\times 22}=14}$

${\displaystyle r_1=r_2+14}$….(ii) 

(𝑖𝑖)𝑖𝑛 (𝑖) ⇒ ${\displaystyle r_1+r_2+14=140}$

⇒ 2𝑟₂ = 126

⇒ 𝑟₂ = ${\displaystyle \frac{126}{2}}$ = 63𝑐𝑚𝑠

𝑟₂ = 63𝑐𝑚𝑠 𝑖𝑛 (𝑖𝑖) 𝑟₁ = 63 + 14 = 77 𝑐𝑚𝑠 

Diameter of circle (i) = 2𝑟₁ = 2 × 77 = 154 𝑐𝑚𝑠

Diameter of circle (ii) = 2𝑟₂ = 2 × 63 = 126 𝑐𝑚𝑠