Question

An 16 16​-oz jar of peanut butter in the shape of a right circular cylinder is 7 7 in. high and 5 5 in. in diameter and sells for ​$ 1.60 1.60. In the same​ store, a 29 29​-oz jar of the same brand is 7 and one half 7 1 2 in. high and 5 and one fourth 5 1 4 in. in diameter. If the cost is directly proportional to​ volume, what should the price of the larger jar​ be? If the cost is directly proportional to​ weight, what should the price of the larger jar​ be? If the cost is directly proportional to​ volume, the price of the larger jar should be ​$ nothing

Answer 1

Explanation:

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

Considering the 16 oz jar,

h = 7 inches

Diameter = 5 inches

Radius = diameter/2 = 5/2

r = 2.5 inches

Volume = 3.14 × 2.5² × 7 = 137.375 inches³

Considering the 29 oz jar,

h = 7.5 inches

Diameter = 5.25 inches

Radius = diameter/2 = 5.25/2

r = 2.625 inches

Volume = 3.14 × 2.625² × 7.5 = 162.27 inches³

1) If the cost is directly proportional to​ volume, then

If 137.375 inches³ cost $1.6

then 162.27 inches³ should cost

(162.27 × 1.6)/137.375 = $1.89

The price of the larger jar would be $1.89

2) If the cost is directly proportional to​ weight, then

If 16 oz cost $1.6, then

29 oz would cost

(29 × 1.6)/16 = $2.9

The price of the larger jar would be $2.9