# Question #f79aa

Feb 12, 2016

$h = 1.91833$

#### Explanation:

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

$v \left(h\right) = \left(14 - 2 h\right) \left(10 - 2 h\right) h$
$v \left(h\right) = 4 {h}^{3} - 48 {h}^{2} + 140 h$

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

$v ' \left(h\right) = 12 {h}^{2} - 96 h + 140 = 0$
$h = 1.91833 \mathmr{and} h = 6.08167$

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.