Rule: y=6πr2 Number of Bags: r=4inches→3bags r=5inches→4bags r=5inches→5bags
Practice makes perfect
We have a concrete forming tube with a volumeV, where V is the product of its length ℓ and the areaA of its circular base.
V=ℓ⋅Abase
We are told that we can make 32ft3 of cement per bag. We need to write a rule to find number of bags of cement needed to fill a tube with ℓ=4 feet and with either r=4 inches, r=5 inches, or r=6 inches.
Writing a Rule for the Volume V of Any Tube
Since the volume V of a tube is the product of its length ℓ and the area A of its circular base with radius r, we can write a rule as follows.
Now, we will write a formula for the number of bags of cement. Then, we will substitute the given radii into that formula. Assume that y is the number of bags of cement. We know that one bag of cement can make Vb=32ft3 and length of the tube we want to fill is ℓ=4ft. Let's use this information!
The formula for the number of bags of cement is y=6πr2. Since the formula is in terms of feet, let's rewrite the given radii in terms of feet. To do so, we will multiply each by the conversion factor of 12in.1ft.
r
Multiply by 12in.1ft
r
4in.
4in.⋅12in.1ft=124ft
≈0.33ft
5in.
5in.⋅12in.1ft=125ft
≈0.42ft
6in.
6in.⋅12in.1ft=126ft
≈0.50ft
Let's start with the 4 inch radius calculation and substitute 0.33 feet for r in the formula.
We cannot use partial bags of cement, so 2.05 should be rounded up to 3 bags of cement. If we follow the same process for the other given radii, we have the following.
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