Use differentials to approximate the amount in cubic feet of paint needed to cover a cube of side length 100 feet if thickness of the paint is to be 0.01 feet.

Question

amistre64 · Answer

differentials?

amistre64 · Answer

add up .01 from 0 to 100; 0 to 100 times, 6 times  is what im thinking but thats integration

amistre64 · Answer

$$\int^{0}_{6}\int_{0}^{100}\int_{0}^{100}\int_{0}^{0.01}du\ dw\ dl\ ds$$

amistre64 · Answer

got my 0 and 6 upside down :)

phi · Answer

There are multiple definitions of differential. http://en.wikipedia.org/wiki/Differential_(infinitesimal) Here they mean infinitesmal quantities

amistre64 · Answer

so summing up all the diffrentials; otherwise known as integration .... right?

phi · Answer

I'm interpreting it as 
each side has a volume of L^2 dh   where L=100, dh= 0.01
and the total volume (ignoring dh^2 and higher terms) is 6*L^2*dh= 600 cu ft