



 
Hi Russell, Suppose D(x) is the density of the concrete x feet up from the bottom. You know that D(x) is a linear function, D(0) = 90 lbs/ft^{3} and D(25) = 50 lbs/ft^{3}. Find the linear function D(x). Suppose that you have thin slab of the concrete, x feet up from the bottom and of thickness Δx feet. The slab is a cylinder so its volume is π r^{2} h = π 10^{2} Δx = 100 π Δx ft^{3}. The density of the slab is D(x) lbs/ft^{3} so its weight is 100 π D(x) Δx. Can you now complete the problem? Since the density varies linearly it seems to me that the weight of the concrete column should be the volume of the column times the density half way up. Does this agree with your answer? Harley  


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