- An ellipsoid is formed by rotating the graph of + y² = 1 about the y-axis. A right circular cone is to be inscribed within the ellipsoid having its circular base parallel to the x-axis as shown in the figure. Let P = (x, y) denote that point of the xy-plane that has a positive x-coordinate and lies on the base of the cone. Carry out the following steps to determine the dimensions of the inscribed cone that has maximal volume. (a) Express the area of the circular base of the cone in terms of x. (b) Express the height of the cone in terms of y. (c) Determine the formula for V, the volume of the cone, as a function of only the variable y. (d) Now use calculus to find the dimensions of the cone having maximal volume. (0, 1) P=(x,y) (2,0) X

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