A = (pi)r^2 word problem: width of walk around pool

[jennal]

The radius of a circular swimming pool is 10ft. A sidewalk of uniform width is constructed around the outside and has an area of 44pi square feet. How wide is the side walk?

I don't think im doing this right but I would appreciate any help. (I dont know how to type the (pi) symbol in.)

r^2 would be 100

44pi + 100 = 144pi

144pi/Pi = pi^2/pi

144 = r^2

r = 12

12 - 10 = 2

The width of the sidewalk is 2 ft

Thank you for taking your time to look over this.

 

[stapel]

The area of a circle with radius "r" is given by "(pi)r²", not just r², so the area of the pool alone cannot be just "100". Also, you cannot combine unlike terms: 100 + 44pi is 100 + 44pi, not 144pi. And I don't know where you're getting "144pi/pi = pi²/pi"...? But since pi does not equal 144, this equation is false.

Try using the circle-area formula: Find the (corrected) area of the pool. Add the listed area of the walkway. Since this is a larger circle, work backwards to find the radius of the total area.

You should arrive at the same answer, but this time by legitimate means (so you will get credit for the answer). :wink:

Eliz.

 

[Denis]

2 is correct...but you were lucky!

w = width of sidewalk

pi(10 + w)^2 - pi(10^2) = 44pi
divide by pi:
(w + 10)^2 - 10^2 = 44

I'll let you finish.