Math
posted by Mike on .
How could you change the height of a cone so that its volume would remain the same when its radius was tripled?

anything that has straight sides and a pointy top has volume = (1/3)(area of base)(altitude)
old V = (1/3) h pi r^2
new V =(1/3) H pi R^2
if new V = old V
then
h r^2 = H R^2
H = h (r/R)^2
H/h = (1/3)^2
H/h = 1/9