Question

Question #f79aa

Answer 1

`h = 1.91833`

Explanation:

Volume = v(h)
v(h) = length x width x height

`v(h) = (14-2h) (10-2h) h`
`v(h) = 4h^3 - 48h^2 +140h`

Volume will be maximum when the derivative of v(x) equals zero.

`v'(h) = 12h^2 - 96h +140 = 0`
`h = 1.91833 or h= 6.08167`

Since plugging h = 6.08167 will give us the width of about 2 and height of 6.08, the first answer of 1.918 makes more sense than 6.081.