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

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.

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