Question

A circular flower garden has an area of $314 {m^2}$. A sprinkler at the centre of the garden can cover an area that has a radius of 12m. Will the sprinkle water the entire garden? (Take $\pi $ = 3.14)

Answer 1

Hint: Here, we will apply the formula of the area of the circle that is A = $\pi {r^2}$ to find out how much area can a sprinkler cover of the garden and then compare it with the area of the flower garden.

Complete step-by-step answer:
A sprinkler can cover an area that has a radius(r) of 12m.
               

We will apply area of circle because a sprinkler will cover an area which is circular in shape
Area of circle that sprinkler can cover = $\pi {r^2}$
= \[3.14 \times {(12)^2}\]$\left[ {\pi = 3.14} \right]$
= $3.14 \times 12 \times 12$
= $\dfrac{{45216}}{{100}}$ = $452.16 {m^2}$
So, Yes, The sprinkle can easily water the entire garden because it can cover an area up to $452.16 {m^2}$ which is more than the area of a circular flower garden with $314 {m^2}$

Note: Alternative method
 Area of a circular flower garden = $\pi {r^2}$
$314$= $3.14 \times {r^2}$ $\left[ {\pi = 3.14} \right]$
\[314 = \dfrac{{314}}{{100}} \times {r^2}\]
Now by doing cross multiplication, we get
$\dfrac{{314 \times 100}}{{314}} = {r^2}$
When we divide 314 by 314, we get 1
$100 = {r^2}$
$\sqrt {100} = r$
Taking the square root of 100, we get
10 = r
So, Radius of the flower garden is 10 m which is smaller than the radius covered by the sprinkler of the garden.
$\therefore $ The sprinkle can easily water the entire garden.