A designer of decorative art plans to market solid gold spheres encased in clear crystal cones. Each sphere is of fixed radius R and will be enclosed in a cone of height h and radius r. See the illustration. Many cones can be used to enclose the sphere, each having a different slant angle θ .The volume V of the cone can be expressed as a function of the slant angle θ of the cone as

What volume V is required to enclose a sphere of radius 2 centimeters in a cone whose slant angle θ is 30°? 45°? 60°?

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(1 + sec 0) V (0) = TR³. (tan 0)² 0° < 0 < 90° 3