Question

1. a company produces two different sizes of soup cans. the volume of the cans varies jointly with the square of the cans radius and the height. the smaller can has a height of 5 inches, a squared radius of 4 inches, and a volume of about 62.8 cubic inches. what is the volume of the taller can, which has a height of 9 inches and a squared radius of 4 inches? round to the nearest tenth, as needed.

\\( v = 3.1 \\) cubic inches

\\( v = 36.0 \\) cubic inches

\\( v = 91.3 \\) cubic inches

\\( v = 113.0 \\) cubic inches

Explanation:

Step1: Define joint variation formula

Joint variation means $V = k r^2 h$, where $k$ is the constant of proportionality, $V$ is volume, $r^2$ is squared radius, and $h$ is height.

Step2: Solve for constant $k$

Substitute $V=62.8$, $r^2=4$, $h=5$:
$$k = \frac{V}{r^2 h} = \frac{62.8}{4 \times 5} = \frac{62.8}{20} = 3.14$$

Step3: Calculate taller can's volume

Substitute $k=3.14$, $r^2=4$, $h=9$:
$$V = 3.14 \times 4 \times 9 = 3.14 \times 36 = 113.04$$

Step4: Round to nearest tenth

$113.04$ rounds to $113.0$

Answer:

$V = 113.0$ cubic inches