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=(W)/(h.r^2)`
Replacing by all the appropiate values we get:

`k=(16)/((1.5)^2.4)\approx1.78`
For the second part knowing k we have:

`W=(16* 4.5* 2^2)/((1.5)^2* 4)=32 ounces`