Nestor R. answered • 07/22/19
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Statistician with a very good grounding in Algebra
I take it the shape is that of a cylinder. V(cylinder) = pi*r2*h (1).
V given as 28.125 m3 and the height h is 2 m greater than the radius r.
Rewrite (1) as V = pi*r2*(r+2), where r+2 is the height.
In (1), divide V by pi to get 28.125/3.142 = 8.951
8.951 = r3 + 2r2 ==> r3 + 2r2 - 8.951 = 0 (2). Solve this cubic equation for r.
r must be less than 2 but greater that 1.5.
By trial and error, r = 1.581m
Plug in r=1.581 into (1) to get V = 3.142*(1.581)2(1.581+2) = 3.142*2.4996*3.581 ~ 28.124 which is very close to the given volume.
Nestor R.
Mark, I tried finding a more rigorous way to solve, but realized that as you suggested sometimes trial and error is easier as long as you can narrow down the choices as early as possible.
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07/22/19
Mark H.
I got the same answer by using an online "equation solver". I was struggling to see if there was a direct way to solve it. Sometimes, I'll do "trial and error" using a spreadsheet07/22/19