SOLUTION: You can make 2/3 cu ft of cement per bag. Write a rule to find the number of bags of cement needed to fill a tube 4 ft long as a function of its radius r. How many bags are needed

Question 953393: You can make 2/3 cu ft of cement per bag. Write a rule to find the number of bags of cement needed to fill a tube 4 ft long as a function of its radius r. How many bags are needed to fill a tube with a 4 in radius?
(please show work)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The Volume(V) of a cylinder(tube) = pi*r^2*l, where r is its radius, l is its length, pi = 22/7
we are given
V = pi*r^2*4
1) we know that each bag of cement can make 2/3 cu foot of cement, therefore
number of bags of cement needed = (pi*r^2*4) / (2/3) = (12*(22/7)*r^2) / 2
number of bags of cement needed = (132*r^2) / 7 = (18.857142857)*r^2
2) we assume the tube is 4 feet long, note 4 inches is 1/3 foot
V = pi*((1/3)^2)*4 = (22/7)*(1/9)*4 = 1.396825397 cubic foot
number of bags of cement = (1.396825397) / (2/3) = 2.095238096
*********************
check the answer with the formula from 1)
number of bags of cement needed = (18.857142857)*(1/3)^2 = 2.095238095
our checks with 1)

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