Question

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

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 $radius = \dfrac{{Diameter}}{2}$
So, putting $Diameter = 1.06m$
$\
  Radius = \dfrac{{1.06}}{2}m \\
   = 0.53m \\
\ $
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 $\pi = \dfrac{{22}}{7}$we will get the area as :
$\
  A = \pi {r^{^2}} \\
   = \dfrac{{22}}{7} \times {\left( {0.53} \right)^2} \\
   = 0.8833{m^2} \\
\ $

So, the area of the circle comes out to be $0.8833{m^2}$. 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 = $0.8833{m^2}$to the correct three significant figures the correct area will be:
$0.883{m^2}$.

Hence the area of the circle will be $0.883{m^2}$, 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.