To answer this question, we need to understand the relationship between the radius and the area of a circle.
The formula for the area of a circle is given by:
[ A = \pi r^2 ]
Where A is the area and r is the radius of the circle.
Now, let's consider the effect of diminishing the radius by 10%.
If the radius is diminished by 10%, it means the new radius is 90% of the original radius. Mathematically, we can express this as:
[ \text{New radius} = 0.9 \times \text{Original radius} ]
Now, let's find the new area of the circle using the new radius.
[ \text{New area} = \pi \times (\text{New radius})^2 ]
[ \text{New area} = \pi \times (0.9 \times \text{Original radius})^2 ]
[ \text{New area} = \pi \times 0.81 \times (\text{Original radius})^2 ]
Now, let's calculate the ratio of the new area to the original area.
[ \frac{\text{New area}}{\text{Original area}} = \frac{\pi \times 0.81 \times (\text{Original radius})^2}{\pi \times (\text{Original radius})^2} ]
[ \frac{\text{New area}}{\text{Original area}} = 0.81 ]
Therefore, if the radius of a circle is diminished by 10%, its area is diminished by 0.19 or 19%.
Option B) 0.19 - This option is correct because it represents the correct percentage decrease in the area of the circle when the radius is diminished by 10%.
The correct answer is B) 0.19.