Come in a cone A right circular cone is inscribed inside a larger right circular cone with a volume of 150 cm3. The axes of the cones coincide and the vertex of the inner cone touches the center the heights of the cones that maximizes the volume of the inner cone.

Solution 49E Step 1: We have to find the ratio of heights of outer cone and inner cone Suppose the base radius and height of cone are R and H And r and h be the base radius and height of inner cone 3 We have given the volume of outer cone V = 150cm Step 2: According to given data the figure is as follows Step 3: The sides of similar triangle are in proportion R = r H Hh Solving this for h H h = Rr h = H Hr R Now the volume of the inner cone is V i r h2 = r (H Hr) R 3 V i r H Hr R