The sum of the radii of two circles is 140 cm and the difference of th

1.	The sum of the radii of two circles is 140 cm and the difference of their circumference is 88 cm. Find the diameters of the circles.
Answer» Let the radii of the two circles be r₁ and r₂. And, the circumferences of the two circles be C₁ and C₂. We know that, circumference of circle (C) = 2πr Given, Sum of radii of two circle i.e., r₁ + r₂ = 140 cm … (i) Difference of their circumference, C₁ – C₂ = 88 cm 2πr₁ – 2πr₂= 88 cm 2(22/7)(r₁ – r₂) = 88 cm (r₁ – r₂₎ = 14 cm r_{1 =} r₂ + 14….. (ii) Substituting the value of r₁in equation (i), we have, r₂+ r₂ + 14 = 140 2r₂ = 140 – 14 2r₂= 126 r₂ = 63 cm Substituting the value of r₂in equation (ii), we have, r₁= 63 + 14 = 77 cm Therefore, Diameter of circle 1 = 2r₁= 2 x 77 = 154 cm Diameter of circle 2 = 2r₂= 2 × 63 = 126 cm

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

Answer»

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

And, the circumferences of the two circles be C₁ and C₂.

We know that, circumference of circle (C) = 2πr

Given,

Sum of radii of two circle i.e., r₁ + r₂ = 140 cm … (i)

Difference of their circumference,

C₁ – C₂ = 88 cm

2πr₁ – 2πr₂= 88 cm

2(22/7)(r₁ – r₂) = 88 cm

(r₁ – r₂₎ = 14 cm

r_{1 =} r₂ + 14….. (ii)

Substituting the value of r₁in equation (i), we have,

r₂+ r₂ + 14 = 140

2r₂ = 140 – 14

2r₂= 126

r₂ = 63 cm

Substituting the value of r₂in equation (ii), we have,

r₁= 63 + 14 = 77 cm

Therefore,

Diameter of circle 1 = 2r₁= 2 x 77 = 154 cm

Diameter of circle 2 = 2r₂= 2 × 63 = 126 cm