If the cost is directly proportional to volume, what should the price of the larger jar be?

Question

an 16oz jar of peanut butter in the shape of a right circular cylinder is 5in high and 3in in diameter and sells for $1.60. In the same store, a 26ounce jar of the same brand is 5 1/2in high and 3 1/4in 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?

Answer 1

Volume of a right circular cylinder:  πr²h

r = d/2 = 1.5 inches

h = 5 inches

 

Cost =  (πr²h)k   where k is the constant of proportion

 

1.60 = π(1.5)²(5)k

 

k = 1.6/[π(1.5)²(5)] = 0.045271

 

So the formula is:  Cost = 0.045271(πr²h)

 

For 5.5 inches high, and 3.25 inches diameter:

r = 1.625

 

Cost = π(1.625)²(5.5)(0.045271) = $2.07

 

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Weight:   Cost = kw   where w is weight and k is constant of proprotionality

 

1.6 = 16k

k = 1.6/16

k = 0.1

 

Cost = 0.1w

 

c = 0.1(26) = $2.60