### Instruction: A jar of peanut butter which is 3 inches in diameter and 4 inches high sells for $\$$0.60. At the same rate, what would be the price for a jar that is 6 inches in diameter and 6 inches high?### Response: The first thing I notice is that the problem is asking about the rate of peanut butter, which depends on the volume of the jar.
I know that the volume of a cylinder is given by the formula V = pi * r^2 * h, where r is the radius and h is the height.
To find the rate of peanut butter, I need to divide the price by the volume.
For the first jar, the radius is half of the diameter, so r = 3/2 inches.
The height is 4 inches.
So the volume is V = pi * (3/2)^2 * 4, which is approximately 28.27 cubic inches.
The rate of peanut butter is then 0.60 / 28.27, which is approximately 0.021 dollars per cubic inch.
For the second jar, the radius is 6/2 = 3 inches and the height is 6 inches.
The volume is V = pi * 3^2 * 6, which is approximately 169.65 cubic inches.
To find the price of the second jar, I need to multiply the rate by the volume.
The price is 0.021 * 169.65, which is approximately 3.56 dollars.