Question

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A circular flower garden has an area of 314m². A sprinkler at the centre of the garden can cover an area that has a radius of 12cm . Will the sprinkler water the entire garden.

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Answer 1

Given : area = 314 m2

According to given condition 

π×r2= 314.

r2=100

∴r=10

Since Sprinkler can cover the garden with a radius of 12m as the radius of the circular garden is only 10m

∴ Sprinkler can water the entire garden.

Answer 2

Correct Question -

A circular flower garden has an area of 314m². A sprinkler at the centre of the garden can cover an area that has a radius of 12m . Will the sprinkler water the entire garden?

Given -

• Area of park is 314m²

• Radius of sprinkler is 12m

To -

• Tell whether the sprinkler can water the entire garden or not.

Formula used -

• Area of circle

Solution -

In the Question, we are provided with the area if circular garden and it's stated that a sprinkler is at the center of the garden, having the radius of 12m, and we need to find, whether it will sprinkle the entire garden or not. For that we will apply the formula of area of circle, and then will find the radius of circle, after that we will come to a conclusion.

According to question -

$\longrightarrow$ Area of circle (a) = 314m²

$\longrightarrow$ Radius of Circle = r

$\longrightarrow$ Radius of sprinkler = 12m

Area of Circle -

$\bf\longrightarrow \: \pi \: {r}^{2}$

On substituting the values -

$\bf\longrightarrow \: a \: = \dfrac{22}{7} \: \times {(r)}^{2} \\ \\ \bf \longrightarrow \: 314 {m}^{2} = \dfrac{22}{7} \: \times {(r)}^{2} \\ \\ \bf \longrightarrow \: 314 {m}^{2} = 3.14 \: \times {(r)}^{2} \\ \\ \bf \longrightarrow \: {(r)}^{2} = \dfrac{314}{31.4} \\ \\ \bf \longrightarrow \: {(r)}^{2} = 100 \: m \\ \\ \bf \longrightarrow \: r \: = \sqrt{100 \: m} \\ \\ \bf \longrightarrow \: r \: = 10m$

Conclusion -

As we can see that the radius of sprinkler is more than the radius of circular garden, $\therefore$ The sprinkler can sprinkle water to the entire circular garden.

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