- #1
Martin Spasov
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Homework Statement
A coat of paint of thickness 0.02 in is applied to the faces of a cube whose edge is 10 in, thereby producing a slightly larger cube. Use differentials to find approximately the number of cubic inches of paint used. Also find the exact amount used by computing volumes before and after painting.
Homework Equations
V = x3
f'(x) = 3x2
dy = f'(x)dx
The Attempt at a Solution
dy = 3*102*0.02 = 6
However the actual solution is 12 (from the answers). Even when doing it manually :
6 * 102 * 0.02 = 12
When I compute the volume before and after I get the same result as before :
10.023 - 103 = 6.012008
I can clearly see that there is factor of 2 difference, but why ? I used the formula and did not get the solution, what exactly was not ok ?
p.s. first post, if I did something wrong, please point it out :)