Answer :
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
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