geometry: volume of cone
posted by Anonymous on .
If the radius of a cone is cut in half, the volume of the cone is multiplied by what number?

recall that volume of cone is given by
V = pi*(r^2)*h/3
where
pi = 3.14 (constant)
r = radius
h = height
if r becomes (1/2)r,
V,new = pi*[(1/2)r]^2*h/3
V,new = 1/4[pi*(r^2)*h/3]
V,new = (1/4)V
thus multiplied by 1/4.
hope this helps~ :) 
original volume = (1/3)π(r^2)h
new volume = (1/3)π(r/2)^2 h = (1/3)π((r^2)/4)h
so multiplied by 1/4