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?
oops , typo
6 x 60cents = $3.60
volume = π(1.5)^2 (4)
= 9π cubic inches
volume of new jar π(3^2)(6) = 54π cubic inches
which is 6 times the original
So the new one should cost 6(.60) or $3.00
Thanks Reiny and Bosian!!!
Well, peanut butter sure knows how to spread its prices, doesn't it? Now, let's do some nutty math! If the first jar is 3 inches in diameter and 4 inches high, and it costs $0.60, we can calculate its volume and then figure out the price for the jar that is 6 inches in diameter and 6 inches high.
The volume of the first jar would be π x (radius)^2 x height, which is π x (1.5)^2 x 4 = 18π cubic inches.
Now, we need to find the volume of the second jar. Since it's double the size, the radius and height will both double. So, the volume would be π x (3)^2 x 6 = 54π cubic inches.
Since the price is proportional to the volume, we can set up a proportion:
(Price of second jar) / (Price of first jar) = (Volume of second jar) / (Volume of first jar)
Let's solve it:
(Price of second jar) / ($0.60) = (54π) / (18π)
Simplifying, we get:
(Price of second jar) = ($0.60) x (54) / (18) = $1.80.
So, the price for a jar that is 6 inches in diameter and 6 inches high would be $1.80. Get ready to spread some laughter and peanut butter!
To solve this problem, we need to find the relationship between the sizes of the jars and their prices. In other words, we need to determine how the price changes as the size of the jar increases or decreases.
The most common way to determine the relationship between variables is through proportions. Proportions compare two ratios and tell us how they are related. In this case, we can set up a proportion between the diameters and heights of the jars, and their respective prices.
Let's first write down the proportion using the given information:
(diameter of first jar)/(diameter of second jar) = (height of first jar)/(height of second jar) = (price of first jar)/(price of second jar)
Let's now plug in the known values:
3/6 = 4/6 = 0.60/x
Now, we can simplify the equation and solve for x, which represents the price of the second jar:
1/2 = 2/3 = 0.60/x
To solve for x, we can use cross-multiplication:
(1/2) * x = 0.60 * 2
x/2 = 1.20
Now, multiply both sides of the equation by 2 to isolate x:
x = 1.20 * 2
x = 2.40
Therefore, the price for a jar that is 6 inches in diameter and 6 inches high would be $2.40.
V = ( d ^ 2 * pi / 4 ) * h
V1 = ( 3 ^ 2 * pi / 4 ) * 4 = ( 9 * pi / 4 ) * 4 = 36 * pi / 4
V2 = ( 6 ^ 2 * pi / 4 ) * 6 = ( 36 * pi / 4 ) * 6 = 216 pi / 4
V2 / V1 = ( 216 * pi / 4 ) / ( 36 * pi / 4 ) = 216 / 36 = 6
6 * 0.6 $ = 3.6 $
OR
V = ( d ^ 2 * pi / 4 ) * h
V1 = ( 3 ^ 2 * pi / 4 ) * 4 = ( 9 * pi / 4 ) * 4 = 9 pi in ^ 3
V2 = ( 6 ^ 2 * pi / 4 ) * 6 = ( 36 * pi / 4 ) * 6 = 216 pi / 4 = 54 pi in ^ 3
V2 / V1 = 54 pi / 9 pi = 54 / 9 = 6
6 * 0.6 $ = 3.6 $