Maths Homework
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Problem: an estimator at a softdrink company must investigate what dimensions (height and radius) a 375mm soft drink can should be to minimize the total surface area of the can. Info provided is:
H
*Surface area of can is= 2πrsq + 2πrh
*volume of the can is=TTrsqh
Q3) it is difficult to work with two variables (h and r) so find the expression for the surface area in terms of the radius (r). to do so
a) Re arrange the formula for volume so that h is the subject? b) Substitute this value for h into the formula for surface area, and simplify where possible. (Note: all steps in your working must be shown.)
Q4) a) using your graph, determine the approximate dimensions (height and radius) of the can with the least surface area?
Q5) Wikepedia suggests that 1.1 million cans of coke are sold each day, (just cans no other products) if they manufactured cans that were optimised for 375ml, how much would they save, considering current practice , each year if the cost of aluminium sheet is $34.60Msquared
Sorry but after I finished the post I noticed that the questuin is for the Casio FX0115ES while I decribed the calculator part for the TI84PLUS. However, the procedure is valid for any calculator that can generate a table from a given function. You should be able to implement it on the Casio. Just read the part that tells you how to create a table from a function: You should look at MODE TABLE
V=Pi*(r^2)*h
which gives h=V/(Pi*r^2)
Take this expression for h and substitute in the expression for the total surface. This gives (after simplifications)
S=2*Pi*r^2 +2*V/r
Open the table setup editor (Read your manual for the Casio)
Press [2nd][WINDOW] to access the Tabble setup
Set table start =2
Set DeltaTbl=0.05 (You can take a smaller value if you want)
Set Indepnt to Auto
Set Depend to Auto
Press [2nd][QUIT] to return to main calculator screen
Open the [Y=] editor
Enter the expression for the surface above as Y1=, using X as variable Y1= 2*Pi*X^2 +2*375/X
Press [2nd][GRAPH] to create the (table)
This part is not calculator-specific
Display the table and, scroll down examining the Y1 values.
Find the value of X (ie r) where the Y1 value is the smallest.
The value of X (r) you read to the left of of the minimum value of Y1 is in centimeters (because 375 mL= 375 cm^3)
The r-value that minimizes the surface should be around 3.90cm
Substitute this value for r in the expression for h above, calculate the value of h.
Please give me an answer about learning outcomes for area and volume
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Shouldn't you try to solve the problem with pen and paper? What will you learn if somebody else does your homework for you? Who gets the credits?. Read your lesson about minimization and get to work.
find the volume and the total surface area of a regular tetrahedron in which the measures of one edge is 10m
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