If a cone has a height that equals twice the diameter of its base, what is its volume in terms of the height

The volume of the cone can be calculated as follows:
volume of cone = (1/3) x pi x (radius)^2 x height > equation 1

We know that the height is twice the diameter, therefore:
h = 2d > equation 2

we also know know that the radius is half the diameter:
r = (1/2) d
d = 2r > equation 3

Substitute with equation 3 in equation 2, we get:
h = 2d = 2 (2r)
h = 4r
 r = (1/4) h> equation 4

Substitute with equation 4 in equation 1, we get:
volume of cone = (1/3) x pi x (radius)^2 x height
                         = (1/3) x pi x (0.25 h)^2 x h
                         = (1/3) x pi x (1/16) h^2 x h
                         = (1/48) x pi x h^3

They are all decomposition reactions.