Problema Solution
jim wants some cans made for him. He visits the Can-Don Can company and asks about making cans. They show him their new line of extruded cans and tell him that the Height of the can is equal to the circumference of the bace. The price is perfect so he orders 500 cans of 10.68 gallons each. What is the radius of the can base?
Answer provided by our tutors
We will assume that the cans have cylinder shape.
1 gal = 231 in^3
10.68 gal = 10.68*231 in^3
10.68 gal = 2467.08 in^3
Let 'r' represent the radius of the base.
The height of the can is equal to the circumference that is: h = 2*r*pi
The volume of the can is: V = r^2*pi*h
Plug h = 2*r*pi for the height in the volume formula and we get:
V = r^2*pi*2*r*pi
V = 2*r^3*pi^2
We also know that the volume of one can is V = 2467.08 in^3 thus we have
2*r^3*pi^2 = 2467.08
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click here to see the equation solved for r
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r = 5 in
The radius of the can base is 5 inches.