Three Dimensional Shapes Question
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Grade 11 Three Dimensional Shapes CCSS: HSG-SRT.C.8, HSG-MG.A.3
The largest cone that will fit in a sphere will be inscribed in the sphere; that is, the cone's apex will touch the sphere, and the circumference of its base will also touch the sphere.
Consider a cross section of the cone inscribed in the sphere, one that intersects the center of the sphere and is perpendicular to the base of the cone. What is the relationship between the radius of the sphere, the radius of the cone, and the height of the cone? (Hint: use the Pythagorean Theorem). Also, state the restrictions on the height and radius of the cone.
Consider a cross section of the cone inscribed in the sphere, one that intersects the center of the sphere and is perpendicular to the base of the cone. What is the relationship between the radius of the sphere, the radius of the cone, and the height of the cone? (Hint: use the Pythagorean Theorem). Also, state the restrictions on the height and radius of the cone.