Question

An elliptical culvert is 3.5 feet tall and 6 feet wide. It is filled with water to a depth of 0.95 feet. Find the width of the stream.

Answer 1

`W_s \approx5.3`

Explanation:

From the question we are told that

Height
`H=3.5ft`

Weight
`W= 6ft`

Depth
`D=0.95ft`

Generally the equation for ellipses is given as

`(x^2)/(a^2) +(y^2)/(b^2) =1`

Where

`b=H/2\\b=3.5/2\\Therefore\\b=1.75\\a=W/2\\a=6/2\\Therefore\\a=3\\`

`(x^2)/(3^2) +(y^2)/(1.75^2) =1`

Generally to find y in the equation
`(x^2)/(a^2) +(y^2)/(b^2) =1`

`y=-b+d`

`y=-1.75+0.95`

`y=-0.8`

Therefore

`(x^2)/(3^2) +((0.8)^2)/(1.75^2) =1`

`(x^2)/(3^2) =1-((0.8)^2)/(1.75^2)`

`(x^2)/(3^2) =1-0.2089795918`

`X^2 =3^2(1-0.2089795918)`

`X^2 =7.119183674`

`X =√(7.119183674)`

`X =2.66817984`

Therefore the width of the given stream is

`W_s=2.66817984*2`

`W_s=5.33635968`

`W_s \approx5.3`