Express the volume V of the cone as a function of h.

Question

If the height, h, of a right circular cone is 6 times the radius, r of its base, express the volume V of the cone as a function of h.

Answer 1

Since the radius is 1/6 of the height h we can express r as h/6

 

Now we need to remember that the volume of a cone  given by

 

V = 1/3 * pi * r^2 * h

 

V = (1/3) * pi * (h/6) ^ 2 * h

 

V = pi * (h^3/108) 

 

V = (3.142h^3) / 108 

 

thats our volume expressed in terms of h Or as a function of h.