Question

What distance does Sunil cover if he takes 6 rounds of a circular garden whose area is $12\dfrac{4}{7}sq.km$? (Take $\pi = \dfrac{{22}}{7}$)

Answer 1

Hint: The area of the circular garden given is $12\dfrac{4}{7}sq.km$. Equate this value with the formula of the area of the circle to find the radius of the circular garden. And using the radius, find the circumference of the circular garden and multiply the result with 6 to get the required length of 6 rounds of the circular garden.

Complete step-by-step answer:
Area of the circle is $\pi {r^2}$, where r is the radius of the circle and the value of $\pi = \dfrac{{22}}{7}$
Circumference of the circle is $2\pi r$, where r is the radius of the circle and the value of $\pi = \dfrac{{22}}{7}$

We are given that area of a circular garden is $12\dfrac{4}{7}sq.km$
We have to calculate the distance Sunil covers if he takes 6 rounds of a circular garden.
As the garden is circular, we have to use the area and circumference of the circle formulas.
Area of the circle is $\pi {r^2}$, where r is the radius of the circle and the value of $\pi = \dfrac{{22}}{7}$
But the area is equal to $12\dfrac{4}{7}sq.km$, which is in mixed fraction. So, convert it into normal fraction.
Equating the given value of the area with $\pi {r^2}$
$
\pi {r^2} = 12\dfrac{4}{7} \\
12\dfrac{4}{7} = \dfrac{{\left( {12 \times 7} \right) + 4}}{7} = \dfrac{{88}}{7} \\
 \to \pi {r^2} = \dfrac{{88}}{7} \\
 \to \dfrac{{22}}{7}{r^2} = \dfrac{{88}}{7} \\
  \to {r^2} = \dfrac{{88}}{7} \times \dfrac{7}{{22}} \\
  \to {r^2} = 4 \\
  \therefore r = 2km \\
 $
The radius of the circular garden is 2km.
The distance covered by Sunil in 6 rounds around the garden will be 6 times of the circumference of the garden.
$
  D = 6 \times 2\pi r \\
  r = 2km,\pi = \dfrac{{22}}{7} \\
  \to D = 6 \times 2 \times 2 \times \dfrac{{22}}{7} \\
  D = \dfrac{{528}}{7} \\
 \therefore D = 75\dfrac{3}{7}km \\
 $
Therefore, the distance covered by Sunil if he takes 6 rounds around circular garden is $75\dfrac{3}{7}km$

Note: A whole number and a fraction together make a mixed fraction. Instead of writing in decimals one can write the value in mixed fractions. Mixed fraction can be converted into normal fraction; the numerator of the new normal fraction is obtained by multiplying the whole number and denominator and adding the previous numerator to this product. The denominators are the same for both. So be careful in converting mixed fractions into normal and vice versa.