The diameter of a circle is 1.06 m. Calculate the area to an appropriate number of significant figures. Take π= 3.14.

The correct option is 0.882 m².

To find the area of the circle, we first identify the given values from the problem:
The diameter of the circle, d = 1.06 m
The value of π to be used, π = 3.14

First, we find the radius (r) of the circle, which is half of the diameter:

$r=\frac{d}{2}=\frac{1.06\text{ m}}{2}=0.53\text{ m}$

Next, we use the formula for the area (A) of a circle:

$A=\pi r^2$

Substitute the values of π and r into the formula:

$A=3.14\times {\left(0.53\text{ m}\right)}^2$

Calculate the square of the radius:

${\left(0.53\right)}^2=0.2809$

Multiply this value by 3.14 to get the area:

$A=3.14\times 0.2809{\text{ m}}^2=0.882026{\text{ m}}^2$

Now, we must round the result to the appropriate number of significant figures.
The given diameter (1.06 m) has 3 significant figures.
The given value of π (3.14) also has 3 significant figures.
When multiplying or dividing measurements, the final answer should be rounded to the same number of significant figures as the measurement with the fewest significant figures. Therefore, we round our calculated area to 3 significant figures:

$A\approx 0.882{\text{ m}}^2$

Thus, the area of the circle is 0.882 m².