# geometry: volume of cone

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If the radius of a cone is cut in half, the volume of the cone is multiplied by what number?

• geometry: volume of cone -

recall that volume of cone is given by
V = pi*(r^2)*h/3
where
pi = 3.14 (constant)
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~ :)

• geometry: volume of cone -

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

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