Word problem

Question

A peanut butter jar in the shape of a right circular cylinder is 4 inches high and 3 inches in diameter and sells for $1.20 if we assume that the cost is proportional it to the volume how much should a jar 6 inches high and 6 inches in diameter cost

Answer 1

First find the volume that sells for $1.20. 

 

Volume of cylinder is πr²h.

 

Volume = (3/2)²(4)π

           = (9/4)(4)π

           = 9π

 

Now we find the other volume.  This volume will be associated with the cost we want to find.

 

Volume = (3²)(6)π

            = 54π

 

 

Now we set a proportion using the volume and cost.

 

Ratio of volume = ratio of cost

 

9π / 54π = 1.20 / x

 

1 / 6 = 1.20 / x

 

 

where x is the cost of the jar 6 inches high and 6 inches in diameter.  Solve for x.

Answer 2

Volume of h=4" by d=3" jar is (pi)(1.5²)((4) = 9 pi cubic inches using pi(radius²)(height) formula.

 

Volume of 6" by 6" jar is (pi)(3²)(6) = 54pi.

 

The new volume is 6 times greater, so cost ought to be 6(1.20) dollars.