Question

Calculate area enclosed by a circle of diameter $1.06m^2$correct to significant figures.
A. $0.883m^2$
B. $0.0883m^2$
C. $0.88333m^2$
D. $0.8830m^2$

Answer 1

Hint: We will use the geometrical concept of area of circle to calculate the area of the given circle.

Complete step by step solution:
First of all, we are given the diameter of the circle as $1.06m$
Now, as we know that $radius={\displaystyle \frac{Diameter}{2}}$
So, putting $Diameter=1.06m$
$$\begin{gathered} Radius={\displaystyle \frac{1.06}{2}}m \\ =0.53m \end{gathered}$$
Again, area of a circle with radius ‘r’ is given as:
$A=\pi r^2$where, A is the area of the circle an d r is the radius of the circle.
So putting the value of radius = 0.53m and $\pi ={\displaystyle \frac{22}{7}}$we will get the area as :
$$\begin{gathered} A=\pi r^{{}^2} \\ ={\displaystyle \frac{22}{7}}\times {\left(0.53\right)}^2 \\ =0.8833m^2 \end{gathered}$$

So, the area of the circle comes out to be $0.8833m^2$. However, we have to round it off to the number of significant figures in 1.06.
Now since the 0 in 1.06 is between two numbers 1 and 6, it means it will also have significance as a digit.

So, the significant figures in 1.06 are 1,0 and 6.
Therefore, we can conclude by saying that there are a total of 3 significant numbers in 1.06.
Then, rounding off the Area = $0.8833m^2$to the correct three significant figures the correct area will be:
$0.883m^2$.

Hence the area of the circle will be $0.883m^2$, rounded off to 3 significant figures.
Therefore, the correct answer is option A.

Note: While rounding off, the number of significant figures have to be counted very carefully, since 0 is considered as a significant figure if and only if, it lies between two other significant digits in a number, whether decimal or non-decimal.