# Thread: Area of circular pattern question

1. ## Area of circular pattern question

I am uncertain I did this problem correct.
A sprinkler sprays water over a distance of 40' at a angle of 155 deg. What is the area in square feet covered.Area of a circle is (pi)(r^2). The only formula that I have been able to get a value in the listed answers is A=1/2(155 deg.)(40)^2. I suspect I am missing something simple?

2. Originally Posted by cross1933
I am uncertain I did this problem correct.
A sprinkler sprays water over a distance of 40' at a angle of 155 deg. What is the area in square feet covered.Area of a circle is (pi)(r^2). The only formula that I have been able to get a value in the listed answers is A=1/2(155 deg.)(40)^2. I suspect I am missing something simple?
if what you are describing is the sector of a circle ...

$\displaystyle A = \frac{155}{360} \cdot \pi (40)^2$

3. $\displaystyle \pi r^2= \pi(40)^2$ is the area of the entire circle of radius 40'. Since there are 360 degrees in a circle, 155 degrees is $\displaystyle \frac{155}{350}$ of the entire circle.

4. Originally Posted by skeeter
if what you are describing is the sector of a circle ...

$\displaystyle A = \frac{155}{360} \cdot \pi (40)^2$
My mistake for the confusion. The area to determine is a full circle covered by a sprinkler at at angle of 155 deg. The only formula I found to provide a answer within the options is the one for a sector of a circle.

5. Originally Posted by HallsofIvy
$\displaystyle \pi r^2= \pi(40)^2$ is the area of the entire circle of radius 40'. Since there are 360 degrees in a circle, 155 degrees is $\displaystyle \frac{155}{350}$ of the entire circle.
My take on the problem is that 155 deg. is the angle at which the sprinkler sprays water from the intersection of the x,y point. It is possible that my interpretation of the problem is incorrect and the correct formula is the area of a sector formula. This formula does provide a answer within the options for a answer.