Question

The weight of a cylindrical can varies jointly with the height of the can and the square of the can’s radius. A 4 inch high can with a 1.5 inch radius weighs 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

Let the weight of the can be W(h,r),
where
h=height
r=radius, and
k=constant of proportionality
then
W(h,r)=kr^2h

We are given that
W(4,1.5)=k(4^2)(1.5)=16
Then we can solve for
k=16/(4^2*1.5)=1/1.5 or =0.667 approximately