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.

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

To find the volume V of any concrete forming tube, you can use the formula V = l * A, where l represents the length of the tube and A represents the area of its circular base.

Now, let's calculate the area A of the circular base for each given radius of the tube:

1. For a 4-inch radius, the formula to calculate the area of a circle is A = π * r^2, where r is the radius. So, A = π * (4 in)^2.

2. For a 5-inch radius, using the same formula as above, A = π * (5 in)^2.

3. For a 6-inch radius, we can use the formula A = π * (6 in)^2.

To find the number of bags of cement needed for a given volume, you would perform division using the volume and the volume of cement per bag.

Since it's given that 2/3 ft^3 of cement can be made per bag, you divide the volume of the tube by 2/3 ft^3. This can be written as:

Number of bags needed = V / (2/3 ft^3).

By substituting the values of V calculated for each different radius above, you can determine the number of bags needed for each concrete forming tube.