Answers:
a) k = 16/9
b) weight = 32 ounces
Explanations:
a) Since the weight of the can varies jointly with the height and the square of the radius of the can, the ratio of the weight of the can to the product of the height and the square of the radius is always constant.
In terms of equation,
[tex] \frac{\text{weight}}{\text{(height)(radius)}^2} = \text{constant}[/tex]
The constant is called the constant of proportionality, which is represented by k. Mathematically,
[tex]k = \frac{\text{weight}}{\text{(height)(radius)}^2} [/tex]
Since weight = 16, height = 4, radius = 1.5, therefore
[tex]k = \frac{16}{(4)(1.5)^2} = \frac{16}{(4)(2.25)}
\newline \boxed{k = \frac{16}{9}}[/tex]
b) Using the equation for k as stated in a),
[tex]k = \frac{\text{weight}}{\text{(height)(radius)}^2} [/tex] (1)
Since we are computing for the weight, we can multiply both sides of equation (1) by the denominator of the right side of equation (1) so that
weight = k(height)(radius)²
Since height = 4.5, radius = 2, then
weight = (16/9)(4.5)(2)²
= (16/9)(4.5)(4)
= (16/9)(18)
= 32
Therefore, the weight of the can is 32 ounces.
