Question

Starkist tuna company will package tuna fish in 2-L cans. Find the radius and the height of the cans if the cans have a surface area which is less that 980 cm^2.

I have no idea how to go about this, it seems like geometry to me. Can you give me some help? Please.

Answer 1

Sarea=PI*diameter*height + 2PI*(diameter/2)^2

Volume=PI(dia/2)^2 h

put numbers in for volume, Sarea, then solve for height in the volume equation, put that in for height in the Area equation. Solve for diameter.

Answer 2

volume of can = pi(r^2)(h)
2000 = pi(r^2)(h)

Surface area of the can = 2 circles + 1 rectangle, where the length of the rectangle is the circumference of the circle and its height is the height of the can.
so
2pi(r^2) + 2rpi < 980

This is actually a typical Calculus problem, where the question would ask for the dimensions of the can with the minimum surface area to hold 2 L

The way it was worded, there would be an infinite number of solutions.

Answer 3

Is the volume 2L? How can I solve for diameter if I don't have the height?

Answer 4

How do I get the volume?

Answer 5

You solve for diameter after putting in for height (area/2pi(dia/2)^2 into the Area equation.

It is called substitution, having two equations and solving it by substitution.

Answer 6

Zach. The volume was given as 2dm^3 (2liters). Use the 2dm^3, that is essential.

Answer 7

If you want the surface area to be equal to 980 and the volume equal to 2 L or 2000 cm^3
then you end up solving a nasty cubic
pir^3 - 980r + 4000 = 0

I found this handy cubic equation solver
http://www.1728.com/cubic.htm

and obtained two possible solutions:
r = 15.08 or r = 4.34
both give us a volume of 2 L and a surface area of 980 cm^2

So if you want your surface area to be < 980, then any r between 4.34 and 15.08 and its corresponding h = 2000/(pir^2) would give a volume of 2 L and a surface area less than 980 cm^2

Answer 8

I tried to solve for H in the volume equation. so, 2=3.14(r^2)H
divide 2 by 3.14=.64
.64=r^2H
.64/r^2=H

Not sure where to go from here