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?
volume of first jar
= π(1.5)^2 (4) = 9π inches^3
volume of 2nd jar
= π(3^2)(3) = 27π
which is 3 times the volume of the first, so it should cost 3 times as much
3(0.60) = $1.80
I do not get how you got 3times as much when they aren't fully simplified.
To find the price for a jar that is 6 inches in diameter and 6 inches high, we can use the concept of volume similarity.
First, let's find the volume ratio between the two jars. The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
For the first jar with a diameter of 3 inches, the radius would be 1.5 inches (since radius = diameter/2). The volume can then be calculated as follows:
V1 = π(1.5^2)(4) = 18π cubic inches
For the second jar with a diameter of 6 inches, the radius would be 3 inches. The volume can be calculated as follows:
V2 = π(3^2)(6) = 54π cubic inches
Now, we can compare the volume ratios:
V2/V1 = (54π)/(18π) = 54/18 = 3
The volume of the second jar is 3 times that of the first jar.
Since the prices are directly proportional to the volumes, we can conclude that the second jar would cost 3 times the price of the first jar, which is $0.60.
Therefore, the price for a jar that is 6 inches in diameter and 6 inches high would be 3 * $0.60 = $1.80.