Question

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?

Answer 1

With the information given we have:
$W=k.h.r^2$
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:
$k=\frac{W}{h.r^2}$
Replacing by all the appropiate values we get:
$k=\frac{16}{(1.5)^2.4}\approx1.78$
For the second part knowing k we have:
$W=\frac{16\times 4.5\times 2^2}{(1.5)^2\times 4}=32 ounces$