Question

The area between the circumferences of two concentric circles is 2464 cm². If the inner circle has circumference of 132 cm, calculate the radius of outer circle.

Answer 1

For the inner circle : 

Circumference = 2 π r = 132 

2 π r = 132 

`2 xx 22/7 xx "r" = 132`

`"r" = (132 xx 7)/(2 xx 22)`

r = 21 cm

Therefore, radius of inner circle = 21 cm 

Area of inner ci rel e = π r² 

`= 22/7 xx 21 xx 21`

= 1386 cm²

Area of outer circle = area of inner circle + area of concentric circles 

= (1386 + 2464) cm² = 3850 cm²

⇒ π r²  = 3850

⇒ R² = `3850 xx 7/22`

⇒ R²  = 1225

⇒ R = 35 cm

Hence, radius of outer circle = 35 cm