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?

Question

Whitney

Mathematics

22 September, 21:50

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?

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Alaina Gill · 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