Question 254246
depends on the depth of the pool.


If the pool is circular, the formula for volume is {{{pi*r^2*h}}}


you get {{{v = pi*r^2*h}}}


v = 1000 so you get {{{1000 = pi*r^2*h}}}


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


if you solve for r, you get {{{r^2}}} = {{{1000 / (pi*h)}}}


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


r = +/- {{{sqrt(1000/(pi*h))}}}


if you solve for h, you get {{{h = 1000 / (pi*r^2)}}}


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


r = +/- {{{sqrt(1000/(pi*6)) = 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(1000/(pi)) = 17.84124116}}}


{{{graph(600,600,-15,15,-20,20,sqrt(1000/(pi*x)))}}}