A small can of juice contains 16 fl oz. A large can has twice the base circumference of the first. How
much juice is in the large can if both cans are right circular cylinders and the second can is similar
to the first?
V/16 = 2^3/1^3
V/16 = 8
V = 128
(volumes of similar solids are proportional to the cubes of their corresponding sides)
To find the amount of juice in the large can, we first need to determine the dimensions of the large can relative to the small can.
Let's assume that the small can has a base circumference of C. This means that the diameter of the small can is C/π, and the radius is (C/π)/2 = C/(2π).
Since the large can has twice the base circumference of the small can, the base circumference of the large can is 2C. Therefore, the diameter of the large can is 2C/π, and the radius is (2C/π)/2 = C/π.
Since the second can is similar to the first, the ratio of the corresponding dimensions of the large can to the small can is the same for all dimensions. This means that the height of the large can is also twice the height of the small can.
Now, let's calculate the volume of both cans to find out how much juice is in the large can.
The volume V of a right circular cylinder can be calculated using the formula: V = πr^2h, where r is the radius and h is the height.
For the small can, the radius is C/(2π), and the height is the height of the small can, let's say h_small.
The volume of the small can is V_small = π(C/(2π))^2 * h_small = (C^2/(4π)) * h_small.
For the large can, the radius is C/π, and the height is twice the height of the small can, so h_large = 2h_small.
The volume of the large can is V_large = π(C/π)^2 * 2h_small = (C^2/(π^2)) * 2h_small = 2(C^2/(π^2)) * h_small.
Since the small can contains 16 fl oz of juice, we can set up the following equation:
V_small = 16 fl oz.
(C^2/(4π)) * h_small = 16 fl oz.
Now, we can solve for the volume of the large can by substituting the value of V_small into our equation:
2(C^2/(π^2)) * h_small = 16 fl oz.
(C^2/(π^2)) * h_small = 8 fl oz.
Therefore, the large can contains 8 fl oz of juice.
Note: To find the exact value of C, additional information, such as the height of the small can, would be needed.