***Draw a picture***

(a) In general,

(i) By construction, the distance from the small cone's base to the large cone's apex is . The proportion between this length and the small cone's radius is the same as the proportion of height to radius in the large cone: . Thus,

(ii)

(b) In this cone, the radius:height ratio is 3:6, so

(i)

(ii) Differentiating implicitly with respect to t, . So, when ,