SOLUTION: Solve this Variation Problem The volume of a can varies jointly as the heights of the can and the square of its radius. A can with an 8 inch height and 4 inch radius has a volum

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Question 180193: Solve this Variation Problem
The volume of a can varies jointly as the heights of the can and the square of its radius. A can with an 8 inch height and 4 inch radius has a volume of 402.12in^3. What is the volume of a can that has a 2 inch radius and a 10 inch height?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The volume of a can varies jointly as the heights of the can and the square of its radius. A can with an 8 inch height and 4 inch radius has a volume of 402.12in^3. What is the volume of a can that has a 2 inch radius and a 10 inch height?
:
One way to do it:
%284%5E2%2A8%29%2F%282%5E2%2A10%29 = 402.12%2Fx
which is:
%28128%29%2F%2840%29 = 402.12%2Fx
reduced to:
%2816%29%2F%285%29 = 402.12%2Fx
Cross multiply
16x = 5*402.12
:
16x = 2010.6
x = 2010.6%2F16
x = 125.66 cu/in
;
;
Check solution on a calc: enter pi*2^2*10 = 125.66