Question

A circular flower garden has an area of $314m^2$. 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]$
= $3.14\times 12\times 12$
= ${\displaystyle \frac{45216}{100}}$ = $452.16m^2$
So, Yes, The sprinkle can easily water the entire garden because it can cover an area up to $452.16m^2$ which is more than the area of a circular flower garden with $314m^2$

Note: Alternative method
 Area of a circular flower garden = $\pi r^2$
$314$= $3.14\times r^2$ $\left[\pi =3.14\right]$
$$314={\displaystyle \frac{314}{100}}\times r^2$$
Now by doing cross multiplication, we get
${\displaystyle \frac{314\times 100}{314}}=r^2$
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.