let

r be the radius of the cone

d = 2r is the diameter

h = the height of the cone

the diameter is 5 times the height

d = 5*h

2r = 5*h

h = 2r/5

the formula for the volume of the cone V = (the area of the cones base b)*(the height of the cone)/3

V = (1/3)*b*h

b = r^2*pi - the area of the base (circle with radius r)

V = (1/3)*r^2*pi*2*r*(1/5)

V = (2/15)*r^3*pi

V(r) = (2/15)*r^3*pi is the volume of the sad as a function of the radius r.