Let the radius of the circle be “r”.
So, the area of a circle = πr2
If the radius of a circle is diminished by 10%, new radius, r = r – (10% of r)
r = 90% of r
r = (90/100)r
r = 9r/10
We know that the area of a circle is πr2 square units.
Now, substitute r = 9r/10
A = π(9r/10)2
A = π(81r2/100)
Therefore, the change in area = πr2 – π(81r2/100)
A = (19/100)πr2
A = 0.19 πr2
Hence, the area is diminished by 19%.