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
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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) (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 =
:
Vol = length * width * depth
V = 7w * w * ()
V = *
Cancel w
V = 7w()
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 = = 5.6875 ft deep
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