I know when you decrease the height of a cone by half that the volume decreases by half from plugging in the numbers in the formula. However, I don't how to explain in words why a decrease in height by half results in a decrease in the volume by half.
Thanks..
2 answers
The left part equals to the right part from the formula. If you increase or decrease left(right) part the same happens to the other part.
original area: a = 1/3 pi r^2 h
new area, using half the height is
1/3 pi r^2 (h/2) = (1/3 pi r^2 h)/2 = a/2
new area, using half the height is
1/3 pi r^2 (h/2) = (1/3 pi r^2 h)/2 = a/2
1 answer