Find the area of a ring whose outer and inner radii are respectively 23 cm and 12 cm.

Consider the ring as shown in the figure below,

The inner radius of ring is ‘r’ and the outer radius is ‘R’.

Area of inner Circle = πr^{2} and Area of outer Circle = πR^{2}

Where r = 12 cm and R = 23 cm

Area of ring = Area of outer circle – Area of inner circle

Area o ring = πR^{2} – πr^{2} (put values of r & R)

⇒ Area of ring = π(23^{2}) – π(12^{2})

⇒ Area of ring = π(23^{2} – 12^{2}) (taking π common from R.H.S)

⇒ Area of ring = π(529 – 144)

= 1210 cm^{2}

Area of ring is 1210 cm^{2}.

8