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The radius we found was 1.4154683 cm, or 1.4 cm rounded to the nearest decimal point, the interval was found between 1.4 cm and 1.5 cm.
To begin with we had to determine what the total volume (cylinder + half a sphere) would be. Given the information that you at Lakeside will being using 10 grams of powder, and the powder you are using has a mass of .2g/cm? we found the total volume to be 50 cm?.
10 grams * (1 cm? / .2 grams) = 50 cm?
From there we had to form an equation to find the total volume of the half sphere and the cylinder in order to solve for a variable (x).
7?x? + ? (4/3 ? x?) = 50 cm?
(Volume of cylinder + ? volume of cylinder = total volume)
Using this equation we simplified the equation so that it would equal zero and we could make it a function that we could look at graphically...
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