SOLUTION: A cylinderical can is designed to hold a volume of 1000 cm3. If the radius is increased by 25%, what is the corresponding decrease in height so the volume is still 1000 cm3?

Algebra ->  Radicals -> SOLUTION: A cylinderical can is designed to hold a volume of 1000 cm3. If the radius is increased by 25%, what is the corresponding decrease in height so the volume is still 1000 cm3?       Log On


   

Question 470631: A cylinderical can is designed to hold a volume of 1000 cm3.
If the radius is increased by 25%, what is the corresponding decrease in height so the volume is still 1000 cm3?
Could you please show all the steps?
Found 2 solutions by Gogonati, poliphob3.14:
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the cylindrical cane is given by the formula:V=pi%2Ar%5E2%2Ah.
Since the volume does not change we can write:
pi%2Ar%5E2%2Ah%5B1%5D=pi%2A%28.25%29%5E2%2Ar%5E2%2Ah%5B2%5D<=>h%5B1%5D%2Fh%5B2%5D=%28.25%29%5E2=6.25%.
Answer:If the radius is increased by 25% the height is decreased by 6.25%.

Answer by poliphob3.14(115) About Me  (Show Source):
You can put this solution on YOUR website!
When r is increased by 25% it becomes %28125%2F100%29%2Ar and the volume of the can
changed to %28125%2F100%29%5E2.
When h is decreased by x% it becomes %28100-x%29%2F100%2Ah. Since the volume of the
can does not change we write the equation:
%28100%2F125%29%5E2=%28100-x%29%2F100 solving this equation we get:
%2810000%2F125%5E2%29%2A100=100-x<=>x=100-%281000000%2F125%5E2%29<=>x=36
Answer:The height is decreased by 36%.