If the radius of a circle is diminished by 10%, then its area is diminished by:

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%.