SOLUTION: A manufacturer packages vegetables in cans that are in the shape of right cylinders with height 15 centimeters and volume 750 cubic centimeters. If the manufacturer reduces the vol

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Question 1195113: A manufacturer packages vegetables in cans that are in the shape of right cylinders with height 15 centimeters and volume 750 cubic centimeters. If the manufacturer reduces the volume of the cans to 600 cubic centimeters but keeps the area of the base the same, by how many centimeters does the height of the can decrease?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
A manufacturer packages vegetables in cans that are in the shape of right cylinders
with height 15 centimeters and volume 750 cubic centimeters.
If the manufacturer reduces the volume of the cans to 600 cubic centimeters
but keeps the area of the base the same, by how many centimeters does the height
of the can decrease?
~~~~~~~~~~~~~~~~~~~ 

The original volume equation for the cylindrical can is

    750 = B*H,     (1)

where B is the base area and H is the height of the cylinder.


After reducing the volume, the equation has the form

    600 = Bh,      (2)

(the base area is the same; only the height of the cylinder changed from H to h).


Divide equation (2) by equation (1)  (both sides).  You will get  (the base area will be canceled on the way)

    600%2F750 = h%2FH,

or

    h%2FH = 4%2F5,   h = %284%2F5%29%2AH = %284%2F5%29%2A15 = 4*3 = 12.


ANSWER.  After reducing the volume, the height of the cylinder decreased by 15-12 = 3 centimeters.

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The volume is the area of the base, multiplied by the height. If the area of the base stays the same, then the volume is directly proportional to the height.

If the volume is reduced by a factor of 600/750 = 4/5, then the height is reduced by the same factor of 4/5.

ANSWER: (4/5)*15 = 12