Question

The width of a circular road is 28m. The area of the inner circle is $39424{{m}^{2}}$. Find the diameter of the outer circle.
(a) 280m
(b) 28m
(c) 200m
(d) 140m

Answer 1

Hint:Calculate the inner radius of the circle by using the fact that the area of the circle with radius ‘r’ is $\pi {{r}^{2}}$. Calculate the outer radius of the circular road by adding the width of the road to the inner radius of the road. Use the fact that the diameter of the circle is double of the radius of the circle to calculate the diameter of the outer circle.

Complete step-by-step answer:
We have to calculate the diameter of the outer circle of a circular road whose width is 28m and the area of the inner circle is $39424{{m}^{2}}$.
We will first calculate the inner radius of the road.
Let’s assume that the inner radius of the road is ‘r’.

We know that the area of the circle with radius ‘r’ is $\pi {{r}^{2}}$.
Thus, we have $\pi {{r}^{2}}=39424$.
Rearranging the terms of the above equation, we have ${{r}^{2}}=\dfrac{39424}{\pi }={\dfrac{39424}{22 }}\times7=12544$.
Taking the square root on both sides, we have $r=\sqrt{12544}=112m$.
We will now calculate the outer radius of the road. To do so, we will add the width of the road to the inner radius of the road.
Thus, the outer radius of the road is $=112+28=140m$.
We will now calculate the diameter of the outer circle of the road.
We know that the diameter of the circle is double of the radius of the circle.
Thus, the diameter of the outer circle $=2\times 140=280m$.
Hence, the diameter of the outer circle is 280m, which is option (a).

Note: One must be careful about units while calculating the length of the outer diameter of the road. We can also calculate the outer diameter of the road by calculating the inner diameter of the road and then adding the double of width of the road to it.