SOLUTION: If you build a circular pool with a volume of 1000 cubic feet, what is the approximate radius of the pool?

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Question 254246: If you build a circular pool with a volume of 1000 cubic feet, what is the approximate radius of the pool?
Found 2 solutions by ptaylor, Theo:
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of a circular pool is given by pi*r^2*h(in this case h is the depth)---a cylinder. Since you don't specify the depth, the radius can be anything that you want it to be----depending on what value you choose for the depth.
Hope this helps---ptaylor

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
depends on the depth of the pool.

If the pool is circular, the formula for volume is pi%2Ar%5E2%2Ah

you get v+=+pi%2Ar%5E2%2Ah

v = 1000 so you get 1000+=+pi%2Ar%5E2%2Ah

you can solve for r or you can solve for h.

if you solve for r, you get r%5E2 = 1000+%2F+%28pi%2Ah%29

take square root of both sides of equation and you get:

r = +/- sqrt%281000%2F%28pi%2Ah%29%29

if you solve for h, you get h+=+1000+%2F+%28pi%2Ar%5E2%29

assuming the depth of the pool is 6 feet all around, the radius would be:

r = +/- sqrt%281000%2F%28pi%2A6%29%29+=+7.283656204+ feet.

graph of equation for the radius is shown below:

y value represents the radius of the pool.
x value represents the depth of the pool.

you can see that when the depth of the pool is 1 foot, the radius of the pool is:

sqrt%281000%2F%28pi%29%29+=+17.84124116

graph%28600%2C600%2C-15%2C15%2C-20%2C20%2Csqrt%281000%2F%28pi%2Ax%29%29%29