Question

Show the rectangular box with fixed volume V=27 and smallest possible surface area is a cube. Hint: if the sides are x, y, and z, then V=xyz and surface area is given by S=2xy+2yz+2xz. Use the constraint in volume to turn the problem into one of two variables.

Answer #1

1. A six-sided box has a square base and a surface area of 54
m^2. Let V denote the volume of the box, and let x denote the
length of one of the sides of the base. Find a formula for V in
terms of x.
2. What is the maximum possible volume of the box in Problem 1?
Note that 0< x≤3√3.

MATH125: Unit 1 Individual Project Answer Form
Mathematical Modeling and Problem Solving
ALL questions below regarding SENDING A PACKAGE and PAINTING A
BEDROOM must be answered. Show ALL step-by-step calculations, round
all of your final answers correctly, and include the units of
measurement. Submit this modified Answer Form in the Unit 1 IP
Submissions area.
All commonly used formulas for geometric objects are really
mathematical models of the characteristics of physical objects. For
example, a basketball, because it is a...

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