61. Generalized cone problem A cone of height h and radius ris constructed from a flat, circular disk of radius a in. by removing a sector AOC of are length x in, and then connecting the edges OA and OC. a. Find a formula for the volume V of the cone in terms of x and a. b. Findrand h in the cone of maximum volume for a-4, 5, 6, 8. c. Find a simple relationship between r and h that is independent of a for the cone of maximum volume. Explain how you arrived at your relationship.

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.