SOLUTION: The ice cream cones at the convenience store are about 5 inches tall and 2 inches wide. A new "lite" cone will be the same height but only 50% of the volume. How wide will the "lit

Algebra ->  Volume -> SOLUTION: The ice cream cones at the convenience store are about 5 inches tall and 2 inches wide. A new "lite" cone will be the same height but only 50% of the volume. How wide will the "lit      Log On


   

Question 1105324: The ice cream cones at the convenience store are about 5 inches tall and 2 inches wide. A new "lite" cone will be the same height but only 50% of the volume. How wide will the "lite" be?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The volume of a cone is V+=+%281%2F3%29%28pi%29%28r%5E2%29%28h%29 where r is the radius (half the "width") and h is the height.

If the lite cone cuts the volume of the cone by a factor of 2 and the height stays the same, then "r^2" in the formula gets cut by a factor of 2, which means "r" is cut by a factor of the square root of 2.

If the radius is cut by a factor of the square root of 2, then so too is the width of the cone.

So the width of the lite cone is the "original" width, divided by the square root of 2: 2%2Fsqrt%282%29+=+sqrt%282%29.