SOLUTION: A lap pool is designed to be seven times as long as it is wide. If the area of the sides and bottom is 980ft^2, what are the dimensions of the pool if the volume of water it can ho

Algebra ->  Rational-functions -> SOLUTION: A lap pool is designed to be seven times as long as it is wide. If the area of the sides and bottom is 980ft^2, what are the dimensions of the pool if the volume of water it can ho      Log On


   

Question 1111483: A lap pool is designed to be seven times as long as it is wide. If the area of the sides and bottom is 980ft^2, what are the dimensions of the pool if the volume of water it can hold is a max?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A lap pool is designed to be seven times as long as it is wide.
let w = the width
then
7w = the length
let d = the depth of the pool
:
If the area of the sides and bottom is 980ft^2, what are the dimensions of the pool if the volume of water it can hold is a max?
7w^2 + 2(d*w) + 2(d*7w) = 980
7w^2 + 2dw + 14dw = 980
7w^2 + 16dw = 980
16dw = -7w^2 + 980
d = %28-7w%5E2%2B980%29%2F%2816w%29
:
Vol = length * width * depth
V = 7w * w * (%28-7w%5E2%2B980%29%2F%2816w%29)
V = 7w%5E2*%28-7w%5E2%2B980%29%2F%2816w%29
Cancel w
V = 7w(%28-7w%5E2%2B980%29%2F16%29)
I graphed this equation (Can't seem to do it here) and got
w = 7 ft width for max volume
then
L = 7*7 = 49 ft long
d = %28-7%287%5E2%29%2B980%29%2F%2816%2A7%29 = 5.6875 ft deep