SOLUTION: an 18-oz jar of peanut butter in the shape of a right circular cylinder is 5in high and 3in. in diameter and sells for $2.89. In the same store, a 22-oz jar of the same brand is 5

Algebra ->  Volume -> SOLUTION: an 18-oz jar of peanut butter in the shape of a right circular cylinder is 5in high and 3in. in diameter and sells for $2.89. In the same store, a 22-oz jar of the same brand is 5       Log On


   

Question 1073925: an 18-oz jar of peanut butter in the shape of a right circular cylinder is 5in high and 3in. in diameter and sells for $2.89. In the same store, a 22-oz jar of the same brand is 5 1/4 in. high and 3 1/4 in. in diameter. If the cost is directly proportional to volume, what should the price of the larger jar be?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Calculating volumes is not necessary. The same peanut butter would have the same density, no matter the net contents in a jar. The "weight" or masses are given and those alone should be enough information.

If as given the price is based only on volume ( or on mass ), then
18%2F2.89=22%2Fx

18x=2.89%2A22

x=%282.89%2A22%29%2F18

x=3.53
The 22 ounce jar is $3.53.
WRONG ASSUMPTION!



IF the price IS based on volumes then the assumption just used above does not work.
volume for cylinder, h%2A2%2Api%2Ar for height h and radius r.
-
The 18-oz jar is %2845%2F4%29pi or about 11.25pi cubic.inch.
The 22-oz jar is %283549%2F256%29pi or about 13.863pi cubic. inch.

Price of the 22-oz jar
%2813.863%2F11.25%29%282.89%29

highlight%283.56%2Adollars%29
$3.56 dollars