Question (not so much homework)

[shadowboy13]

1. Homework Statement

A square garden has an area of 1764 squared feet, and the gardener wants to install a sprinkler (with a circular spraying pattern) at the center of the garden. What is the minimum radius of spray the sprinkler would need in order to water ALL of the garden.

2. Homework Equations
pi*r squared=1764


3. The Attempt at a Solution
Now my question is... should r not be around 23.70 rounded up? In order for it to cover the entire garden?

Thanks for any help i get :)
(Apologize for lack of latex, but I'm in a hurry)

 

[LCKurtz]

Draw a picture of the square garden. Where would you put the sprinkler?

 

[Curious3141]

Draw a picture of the square garden. Where would you put the sprinkler?

It's already specified that the sprinkler has to be at the centre of the garden.

To the OP, think circumcircle.

 

[Mentallic]

1. Homework Statement

A square garden has an area of 1764 squared feet, and the gardener wants to install a sprinkler (with a circular spraying pattern) at the center of the garden. What is the minimum radius of spray the sprinkler would need in order to water ALL of the garden.

2. Homework Equations
pi*r squared=17643. The Attempt at a Solution
Now my question is... should r not be around 23.70 rounded up? In order for it to cover the entire garden?

Thanks for any help i get :)
(Apologize for lack of latex, but I'm in a hurry)

You've found the radius for a circle that has area 1764. If you draw a square with side length s and a circle (both having equal centres) with radius slightly greater than s/2 (diameter greater than s), then you'll see that their areas must be about the same but we haven't answered the problem which is to find the radius of the circle that would water the entire garden.

If the area of the square garden is 1764ft² then what is the side length of the square? Now, where and what is the furthest distance on the square from the centre of the square?

 

[shadowboy13]

You've found the radius for a circle that has area 1764. If you draw a square with side length s and a circle (both having equal centres) with radius slightly greater than s/2 (diameter greater than s), then you'll see that their areas must be about the same but we haven't answered the problem which is to find the radius of the circle that would water the entire garden.

If the area of the square garden is 1764ft² then what is the side length of the square? Now, where and what is the furthest distance on the square from the centre of the square?

Yeah i realized after reading that where i made a faulty connection.

Oh well, now i know.

 

[adjacent]

1. Homework Statement

A square garden has an area of 1764 squared feet, and the gardener wants to install a sprinkler (with a circular spraying pattern) at the center of the garden. What is the minimum radius of spray the sprinkler would need in order to water ALL of the garden.

2. Homework Equations
pi*r squared=1764


3. The Attempt at a Solution
Now my question is... should r not be around 23.70 rounded up? In order for it to cover the entire garden?

Thanks for any help i get :)
(Apologize for lack of latex, but I'm in a hurry)

As @Mentallic said,The center of both the circle and the square is in the same position.
Here the circle should be larger than the square to water ALL the garden

As you can see,the 1/2 diagonal of the square:Red color line,is the same as the radius of circle.Find it using trigonometry.
First fine the side length of square.Then Use pythagoras Theorem.

 

[shadowboy13]

As @Mentallic said,The center of both the circle and the square is in the same position.
Here the circle should be larger than the square to water ALL the garden

As you can see,the 1/2 diagonal of the square:Red color line,is the same as the radius of circle.Find it using trigonometry.
First fine the side length of square.Then Use pythagoras Theorem.

Yeah i know i pictured it a bit after the fact.

Oddly enough, I've solved far harder problems than that with no issue, yet simple problems always seem to stump me in the high hours of the morning, no more math after midnight :)

Thank you everybody