Question

the diameter of teacher touching circles are 15 cm and 25 CM respectively find the distance between their centres

Answer 1

When two circles touch each other, the two centers and the point of contact are all on one straight line.

If the two circles are touching each other externally, then 
   the distance between centers = sum of radii = 15+25 = 40 cm

If one circle touching the other from inside of the circle, then the distance is difference of radii :  25-15 = 10 cm.

Hope This helps :)

Answer 2

π(R²-r²)
22/7(25²-15²)
Now solve it.. your teacher will be happy