Acan in the shape of a right circular cylinder is to be constructed to contain 1000 cm3. the circular top and bottom ofthe can must have a radius of 0.25 cm more than the radius of the can so that the excess can be used to form a seal with the side. the sheet of material being formed into the side of the can must also be 0.25 cm longer than the circumference ofthe can so that a seal can be formed. find, to within 10^4 , the minimal amount of material needed to construct the can.

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in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

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