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 cubed of concrete per bag of cement. 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? A 5-inch radius?

Part A:

The volume of a cylinder is given by

[tex]V=\pi r^2h[/tex]

where r is the radius of the base and h is the height.

Given that Concrete forming tubes are used as molds for cylindrical concrete supports. The volume of a tube 4 ft. long as a function of its radius r is given by

[tex]V=4\pi r^2[/tex]

Given that 2/3 ft cubed of concrete can be made per bag of cement. Then the number of bags of cement needed to fill a tube 4 ft. long as a function of its radius r is given by:

[tex] \frac{4\pi r^2}{2/3} =6\pi r^2[/tex] bags of cement.

Thus, the number of bags that is needed to fill a tube with a 4-in. radius is given by

[tex]6\pi ( \frac{4}{12} )^2=6\pi ( \frac{1}{3} )^2 \\ \\ =\left( \frac{6}{9} \right)\pi=2.1\ bags\ of\ cement[/tex]



Part B:

Given that 2/3 ft cubed of concrete can be made per bag of cement. Then the number of bags of cement needed to fill a tube 4 ft. long as a function of its radius r is given by:

[tex] \frac{4\pi r^2}{2/3} =6\pi r^2[/tex] bags of cement.

Thus, the number of bags that is needed to fill a tube with a 5-in. radius is given by

[tex]6\pi ( \frac{5}{12} )^2=6\pi ( \frac{25}{144} ) \\ \\ =\left( \frac{25}{24} \right)\pi=3.3\ bags\ of\ cement[/tex]