Question

If circumference of a circle be 8.8 m then its radius is equal to:
(a) 1.60 m approx
(b) 1.61 m approx
(c) 1.4 m approx
(d) None of these

Answer 1

Hint: We have given the circumference of a circle and we are asked to find the radius of the circle. We know that formula for circumference of the circle is equal to $2\pi r$ where “r” is the radius of the circle so equating the value of circumference given in the question to $2\pi r$ and then substitute the value of $\pi =\dfrac{22}{7}$ in this equation and solving this equation will give the value of radius (or r).

Complete step-by-step answer:
We have given the circumference of the circle as 8.8 m and we are asked to find the radius of the circle.
In the below diagram, we have drawn a circle with radius r.

In the above diagram, we have shown radius as AC which is equal to r.
We know that circumference of the circle is equal to:
$2\pi r$
In the above formula, r is the radius of the circle.
Now, equating the circumference of the circle to 8.8 m we get,
Circumference of the circle equal to:
$2\pi r=8.8$………… Eq. (1)
Substituting $\pi =\dfrac{22}{7}$ in the above equation we get,
$\begin{align}
  & 2\left( \dfrac{22}{7} \right)r=8.8 \\
 & \\
\end{align}$
Multiplying 2 by 22 in the left hand side of the above equation we get,
$\left( \dfrac{44}{7} \right)r=8.8$
Dividing 44 on both the sides of the above equation we get,
$\begin{align}
  & \dfrac{r}{7}=\dfrac{8.8}{44} \\
 & \Rightarrow \dfrac{r}{7}=0.2 \\
\end{align}$
Cross multiplying the above equation we get,
$r=1.4m$
From the above calculations, the radius of the circle is equal to 1.4 m.

So, the correct answer is “Option C”.

Note: There is a thought that comes to your mind that instead of putting the value of $\pi $ as $\dfrac{22}{7}$ in eq. (1) we can substitute the value of $\pi $ as 3.14. We have shown the equation (1) below:
$2\pi r=8.8$
The answer is why we chose the value of $\pi $ as $\dfrac{22}{7}$ over 3.14 because as you can see the right hand side of the above equation, you will find that 8.8 is divisible by 22 by 0.4 times whereas if we put $\pi $ as 3.14 then the calculations become complex.