Tuesday

September 23, 2014

September 23, 2014

Posted by **Sejul** on Saturday, December 3, 2011 at 12:36pm.

a) use formula for surface area to express the height h of the box in terms of x.

b) find the dimensions of the box that will produce the maximum volume.

- algebra -
**Steve**, Sunday, December 4, 2011 at 6:28pmside of square = x

height = h

surface area = x^2 + 4xh

x^2 + 4xh = 50

so,

h = (50 - x^2)/4x

v = hx^2 = (50-x^2)/4x * x^2

v = x(50-x^2)/4

v has a max at x = 5sqrt(2/3) = 4.08

so, a box 4 x 4 x 17/8 will have maximum volume of 34

**Answer this Question**

**Related Questions**

calculus - A container company is tasked to make an open-top rectangular box ...

calculus - A box with a square base and an open top is to have a volume of 68in^...

Pre Cal - find the surface area of a box of hieght h whose base dimensions are p...

Physics - An open box with a square base (see figure) is to be constructed from ...

Calculus, Surface Area - An open rectangular box (no top) has a square base with...

calculus - Find the formula for the described function and state its domain. An ...

algebra - Open-top box. Thomas is going to make an open-top box by cutting equal...

Calculus - I actually have two questions: 4. An open box is to be made from a ...

Calculus - Q. An open-top box with a square base is to have a volume of 62.5 ...

MATH - A box with an open top has vertical sides, a square bottom, and a volume ...