Circle circumscribed within a square

[mameha]

I thought I had the correct solution but I'm doing something wrong here:

A circular flower bed lies in a square garden plot that is 60 meters on each side. What fraction of the garden plot area is not part of the flower bed?

A figure is given of the circle (flower bed) circumscribed within a square.

So the diameter of the circle would be equal to 60 m with a radius of 30 m. The fraction of the plot area outside of the flower bed is equal to:

1200 - 900(pi)/1200

This simplifies to:

[4 - 3(pi)]/4

except the correct answer is [4 - pi]/4

Could someone please show me where I'm going wrong here? Thanks in advance!!

 

[axrw]

(60^2 - 30^2 * pi)/60^2

(3600 - 900*pi)/3600

factor out 900

(4 - pi)/4

 

[Mrspi]

I thought I had the correct solution but I'm doing something wrong here:

A circular flower bed lies in a square garden plot that is 60 meters on each side. What fraction of the garden plot area is not part of the flower bed?

A figure is given of the circle (flower bed) circumscribed within a square.

So the diameter of the circle would be equal to 60 m with a radius of 30 m. The fraction of the plot area outside of the flower bed is equal to:

1200 - 900(pi)/1200

This simplifies to:

[4 - 3(pi)]/4

except the correct answer is [4 - pi]/4

Could someone please show me where I'm going wrong here? Thanks in advance!!

The area of the square garden would be 60<SUP>2</SUP>, right?

The area of the circular flower bed, which has a radius of 30, would be

A(flower bed) = pi*30<SUP>2</SUP>

The area that is NOT part of the flower bed is

60<SUP>2</SUP> - [pi * 30<SUP>2</SUP>

or,

3600 - 900 pi

or,

900(4 - pi)

Ok....now, you're asked what part of the garden plot is NOT part of the flower bed.

That looks to me like it would be

(stuff that is not part of flower bed) / (whole garden)

900*(4 - pi) / 36000

Reduce that fraction...I believe you will get

(4 - pi) / 4

I hope this helps you.

 

[mameha]

Sorry it took so long to reply, thanks to you both!!