Inequalities math homework problem

Click For Summary
SUMMARY

The problem involves constructing a rectangular solid using wire along its edges, where the length (L) is twice the width (w) and the total wire used is 40 cm. The equations governing the dimensions are w + L + h = 40 and L = 2w. The volume of the solid must fall between 2 cm³ and 4 cm³, leading to the inequalities w * L * h > 2 and w * L * h < 4. By substituting L into the volume inequality, the range of possible values for the width can be determined.

PREREQUISITES
  • Understanding of algebraic inequalities
  • Knowledge of volume calculations for rectangular solids
  • Familiarity with substitution methods in equations
  • Basic geometry of rectangular solids
NEXT STEPS
  • Explore solving inequalities in one variable
  • Learn about volume formulas for three-dimensional shapes
  • Study substitution techniques in algebra
  • Investigate optimization problems in geometry
USEFUL FOR

Students tackling geometry and algebra problems, educators teaching inequalities, and anyone interested in practical applications of volume calculations in three-dimensional geometry.

xCanx
Messages
44
Reaction score
0
A rectangular solid is to be constructed with a special kind of wire along all
the edges. The length of the base is to be twice the width of the base. The
height of the rectangular solid is such that the total amount of wire used (for
the whole figure) is 40 cm. Find the range of possible values for the width of
the base so that the volume of the figure will lie between 2 cm3 and 4 cm3.
Write your answer correct to two decimal places.

Can someone show me how to start off?
 
Physics news on Phys.org
w=width, L=length, h=height;

w+L+h=40, L=2w

wLh>2 and wLh<4
 

Similar threads

Finding Possible Width Range for a Rectangular Solid with a Given Volume
  • · Replies 1 ·
Replies
1
Views
2K
Adjustment of Significant Figures
  • · Replies 11 ·
Replies
11
Views
2K
MHB Related rates calculus problem about water tank
  • · Replies 2 ·
Replies
2
Views
1K
Measurements Calculation Problem
  • · Replies 3 ·
Replies
3
Views
1K
Rate of change of volume of a rectangular box
  • · Replies 13 ·
Replies
13
Views
29K
Optimization Problem Homework Solution
  • · Replies 2 ·
Replies
2
Views
3K
Solve Triangle Pyramid Volume: V=72cm3, h=12cm
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad The Basic Area Problem (introduction to the topic of integrals)
  • · Replies 24 ·
Replies
24
Views
4K
Fluid Mechanics and Archimedes Principle
  • · Replies 18 ·
Replies
18
Views
2K
I need to find the possible error for the volume of a cuboid
  • · Replies 5 ·
Replies
5
Views
9K