Begin with a circular piece of paper with a4-in. radius as shows in (a). cut out a sector with an arc length of x.Join the two edges of the remaining portion to form a cone with radius r and height h, as shown in (b).
a) Explain why the circumference of the bas eofthe cone is
b) Express the radius r as a function of x.
c) Express the height h as a function of x.
d) Express the volume V of the cone as afunction of x.
a. Identify the equation as representing a circle, an ellipse, a hyperbola, or a parabola.
b. Graph the curve. c. Identify key features of the graph. That is. If the equation represents a circle, identify the center and radius.
If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity.
If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity.
If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the directrix, and equation of the axis of symmetry.