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the weight of a cylindrical can varies jointly with the height of the can and the square of the cans radius. A 4-inch high can with a 1.5 inch radius weights 16 ounces. a) Find the constant of proportionality, k. b) What is the weight of a can made of the same material that is 4.5 inches high and has a 2 inch radius?

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Hummingbeard
With the information given we have:
[tex]W=k.h.r^2[/tex]
Where W is the weight, k is the proportionality constant and r is the radius of the can's radus. Remember that the weight varies jointly so this key word means that you need to multiply the mentiones parameters by a proportionality constant k. 
We simply need to reorganize the expression and isolate k for the frst answer:
[tex]k=\frac{W}{h.r^2}[/tex]
Replacing by all the appropiate values we get:
[tex]k=\frac{16}{(1.5)^2.4}\approx1.78[/tex]
For the second part knowing k we have:
[tex]W=\frac{16\times 4.5\times 2^2}{(1.5)^2\times 4}=32 ounces[/tex]

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