SOLUTION: Constructing a Border around a Pool: A pool in the shape of a circle measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform wid

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Constructing a Border around a Pool: A pool in the shape of a circle measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform wid      Log On


   

Question 499418: Constructing a Border around a Pool:
A pool in the shape of a circle measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Constructing a Border around a Pool:
A pool in the shape of a circle measures 10 feet across.
One cubic yard of concrete is to be used to create a circular border of uniform width around the pool.
If the border is to have a depth of 3 inches, how wide will the border be?
:
Convert 1 cu yd to cu ft: 3^3 = 27 cu/ft
Convert 3 in to .25 ft
Find the area of the circular border:
27%2F.25 = 108 sq/ft
:
Find the area of the pool (radius = 5 ft)
pi%2A5%5E2 = 78.54 sq/ft
then
108 + 78.54 = 186.54 sq/ft is the total area (pool and border)
let r = the overall radius
pi%2Ar%5E2 = 186.54
divide both sides by pi, results
r^2 = 59.38
r = sqrt%2859.38%29
r = 7.7 ft is overall area
subtract the radius of the pool
7.7 - 5 = 2.7 is the width of the concrete border