Question

A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)​

Answer 1

$\huge\mathfrak{\underline{Correct\:question}}$

A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)

___________________________

Given that:-

• 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 12 m.

To find:-

• Will the sprinkler water the entire garden?

We have to take (π = 3.14)

Answer:-

$\bold{STEP-BY-STEP-EXPLANATION}$

From the question it is given that,

Area of the circular flower garden = 314 m^2

Sprinkler at the centre of the garden can cover an area that has a radius = 12 m

Area of the circular flower garden = πr^2

314 = 3.14 × r^2

314/3.14 = r^2

r^2 = 100

r = √100

r = 10 m

∴Radius of the circular flower garden is 10 m.

Since, the sprinkler can cover an area of radius 12 m

Hence, the sprinkler will water the whole garden.

#BAL

#AnswerWithQuality

Answer 2

$\bf{\Huge{\underline{\boxed{\sf{\red{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

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.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The sprinkler water the entire garden.

$\bf{\Large{\underline{\boxed{\rm{\green{Explanation\::}}}}}}$

Let the radius of the garden be R.

We know that area of circle : $\rm{\pink{\pi r^{2} }}$

$\longmapsto\rm{314m^{2} \:=\:3.14*R^{2} }$

$\longmapsto\rm{R^{2}\:=\:\frac{314*100}{3.14*100} }$

$\longmapsto\rm{R^{2} \:=\:\cancel{\frac{31400}{314} m^{2} }}$

$\longmapsto\rm{R^{2} \:=\:100m^{2} }$

$\longmapsto\rm{R\:=\:\sqrt{100m^{2} } }$

$\longmapsto\rm{R\:=\:10m}$

Thus,

$\bf{\large{\boxed{\sf{\blue{The\:sprinkler\:water\:the\:entire\:garden\:is\:10m}}}}}}$