Concrete forming tubes are used as molds for cylindrical concrete supports. The volume V of a tube is the product of its length l and the area A of its circular base. You can make 2/3 ft^3 of cement per bag. Write a rule to find the number of bags of cement needed to fill a tube with a 4-in. radius. A 5-inch radius? A 6-inch radius?

What is a rule for the volume V of any tube?

What operation do you use to find the number of bags needed for a given volume?

Please explain.

1 answer

v = lA = pi l r^2

#bags = v ft^3 * 2/3 bags/ft^3 = 2v/3 bags

I note that none of the tube sizes include the length, but working with the 4" radius, we have

bags(4,l) = 2/3 (pi l (1/3)^2) = 2pi/27 l

do the others likewise