Introduction to Mathematics thinking-project

Introduction to Mathematics thinking-project 1
Australian Catholic University
Introduction to Mathematical thinking
Investigative Project
Name:
Student Number:
Course Code: S00256359

Introduction to Mathematics thinking-project 2
(a). The sketch of the box and its net from which it can be constructed are presented below.
(i)The sketch of the box
h
x
(ii)
x
h
In the net above, I have assumed that the box will be closed on top. Have also assumed that the
sides of the square base are x meters each and the height is h meters.
(b) The formula for the volume and surface are of the box. The volume of the box should be the
same as that of the nuts and bolts which will be packed inside it. We will express the formula of
the box as V. The box is a cuboid with square base of dimensions x meters and a height of h
meters cm. Since we have been provided with the volume as 0.5 cubic meters, we will apply the
formula for calculating the volume of a box.
Let the volume= V
The base square sides=x Meters
The height=h Meters

Introduction to Mathematics thinking-project 3
V= l ×w × h
V=( x × x × h¿=x2 h
V= x2 h=0.5 m3
The formula for the surface area of the box is.( There is the assumption that the box will have a
top)
SA= 2 {( l× w )+ ( l× h ) + ( h ×w ) }
SA=2 {( x × x )+ ( x ×h )+ ( h× x ) }
SA=2 x2+4 xh
(c) We then proceed and find the cost of the material used in the making of the box. The card
board used in making the box costs $0.33 per square meter, The cost of making the box will be
obtained by multiplying the surface area of the cost per square meter of card board. Let the cost
be C.
Cost=$0.33(2 x2+4 xh)
But since we know the volume of the box, we simplify and express the height in terms of width
(x meters)
x2 h=0.5m3, h= 0.5
x2
Replacing the height in the cost equation
C=0.33(2x2+4 x( 0.5
x2 )¿
C=0.66x2+ 0.66
x
(d) Drawing the graph of the cost equation using the Desmos graphing calculator.
Using the equation y=0.66x2+ 0.66
x
Thee graph will be as shown below.