Question

The radius of a circular grass field is 35 m. A 7 m wide road runs round outside the field. Find the area of the road.

Answer 1

Hint: We will get the two circles as per the conditions given in the questions as having radius 35 m and (35 + 7) m. The area of the road will be given as, the area of the bigger circle - area of the smaller circle. We will use the formula for the area of the circle equal to $\pi {{r}^{2}}$, where $\pi =3.14$ and r is the radius of the circle.

Complete step-by-step answer:
It is given in the question that the radius of a circular grass field is 35 m. A 7 m wide runs around the field and we have been asked to find the area of the road. We will first represent the situation given in the question by a figure as given below.

We have been given that the radius of the circular ground is 35 m and the radius of the circular ground and the road together will be = (35 + 7) = 42 m. We know that the area of the circle is given by $\pi {{r}^{2}}$, where $\pi =3.14$ and r is the radius of the circle. Now, we know that we can find the area of the circular road by finding the area of the circular field and the area of the circular field and the road together and then subtracting the area of the circular field from it. So, let us consider the radius of the road and field together as R and the radius of the field as r, then we get the area of the road as,
$\pi {{\left( R \right)}^{2}}-\pi {{\left( r \right)}^{2}}$
Where R = (r + 7) m = (35 + 7) m = 42 m and r = 35 m. So, we get the area of the road as,
$\begin{align}
  & \pi {{\left( 42 \right)}^{2}}-\pi {{\left( 35 \right)}^{2}} \\
 & \Rightarrow 1764\pi -1225\pi \\
 & \Rightarrow 539\pi \\
 & \Rightarrow 539\left( 3.14 \right) \\
 & \Rightarrow 1693{{m}^{2}} \\
\end{align}$
Hence, the area of the road will be $1693{{m}^{2}}$.

Note: The students may assume the given radius of the road as the length of the road and may directly find the area of the road by multiplying the radius of the circular field by 7 m, which would be incorrect. If we use this method then we have to find the perimeter of the circle and then multiply the perimeter of the circle with 7 m to get the area of the road.