# Open-top box form problem

## Description

HP-15C Owner's Handbook - Pages 189-190

Exercise:
Using a rectangular piece of sheet metal 4 decimeters by 8 decimeters, an open-top box having a volume of 7.5 cubic decimeters is to be formed. How should the metal be folded? (A taller box is preferred to a shorter one.)

Solution:
You need to find the height of the box (that is, the amount to be folded up along each of the four sides) that gives the specified volume. If x is the height (or amount folded up), the length of the box is (8 – 2x) and the width is (4 – 2x). The volume V is given by

`V = (8 – 2x)(4 – 2x)x`.

By expanding the expression and then using Horner's method (page 79), this equation can be rewritten as

`V = 4 ((x – 6)x + 8)x`.

To get V=7.5, find the values of x for which

`f(x) = 4((x – 6)x + 8)x – 7.5 = 0`.

Name Description
3

## Program

Line Display Key Sequence
000
001 42,21, 3 f LBL 3
002 6 6
003 30
004 20 ×
005 8 8
006 40 +
007 20 ×
008 4 4
009 20 ×
010 7 7
011 48 .
012 5 5
013 30
014 43 32 g RTN