You are here:

Calculus/precalculus

Advertisement

Expert: Alon Mandes - 9/16/2008


Question
an open box is to be constructed from a rectangular piece of sheet metal 8 by 12 inches by cutting away identical x-inch squares from each of the four corners and folding up the sides. express the volume of the resulting box as a function of x.

Answer
Ok, let's consider the cut of corners :
The area of the cut corners is in a shape of isosceles triangle
with right angle. Le's set y as the limp of this triangle, so we
know that (y^2)/2=x (it's the area of the triangle which is also the
area of the cut corner). Hence, y=root(2)*x.
The folding will be performed in the middle of the diagonal limp
of the corners, in order to get an open box. The volume of such box
will be : [Area of the base X the height].
The height is y/2, meaning x/root(2).
The base area is [8-2y]*[12-2y]. Thus, the volume will be :
V=[x/root(2)]*[8-root(2)x]*[12-root(2)x]
V=[x/root(2)]*[96+2x^2-20root(2)x]

Alon.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

©2012 About.com, a part of The New York Times Company. All rights reserved.