Math CentralQuandaries & Queries


Question from swathi, a student:

A company manufactures aluminum cans. one customer places an order for cans that must be 15 cm high, with a volume of 1200cm cube.

a) use the formula V= pie r squared h to determine the radius that the company should use to manufacture these cans

b) graph the function that corresponds to 0 = pie r squared h minus V to determine the radius.


In the formula $V = \pi \; r^2 h$ you know $h = 15$ cm and $V= 1200$ cubic centimeters. Thus you have

\[1200 = \pi \; r^2 \times 15.\]

For part a) I would divide both sides of the equation by $15 \pi$ and then take the square root.

The equation above can be rewritten as

\[0 = \pi \; r^2 \times 15 - 1200\]

and hence if you graph the function

\[y = \pi \; r^2 \times 15 - 1200\]

the graph will cross the r-axis at the value that corresponds to $y = 0.$

I hope this helps,

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