SOLUTION: A company is changing the size of its ice-cream cones. If the height of a cone is reduced from 8 centimeters to 6 centimeters and its radius is increased from 6 centimeters to 8 ce

Algebra ->  Volume -> SOLUTION: A company is changing the size of its ice-cream cones. If the height of a cone is reduced from 8 centimeters to 6 centimeters and its radius is increased from 6 centimeters to 8 ce      Log On


   

Question 778488: A company is changing the size of its ice-cream cones. If the height of a cone is reduced from 8 centimeters to 6 centimeters and its radius is increased from 6 centimeters to 8 centimeters, what will happen to the volume of the cone?
The volume is reduced to three fourths of the original.
The volume is reduced by four thirds of the original.
The volume remains the same.
The volume is increased by one third of the original.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
V is volume.
h is height, r is radius of base.
For a cone, V=%281%2F3%29h%2Api%2Ar%5E2

Initial V, %281%2F3%298%2Api%2A6%5E2
Changed V, %281%2F3%296%2Api%2A8%5E2

Compare these volumes.
changed V divided by Initial V:
%28%281%2F3%296%2Api%2A8%5E2%29%2F%28%281%2F3%298%2Api%2A6%5E2%29
%286%2A8%5E2%29%2F%288%2A6%5E2%29
%282%2A3%2A2%2A2%2A2%2A2%2A2%2A2%29%2F%288%2A2%2A2%2A3%2A3%29
%282%5E7%2A3%29%2F%282%5E5%2A3%5E2%29
2%5E2%2F3
highlight%284%2F3%29, the ratio of changed to initial volumes.