Question: Solve the following problem with and without calculus. A good picture helps. a. A cube with side length r is inscribed in a sphere, which

Solve the following problem with and without calculus. A good picture helps.

a. A cube with side length r is inscribed in a sphere, which is inscribed in a right circular cone, which is inscribed in a right circular cylinder. The side length (slant height) of the cone is equal to its diameter. What is the volume of the cylinder?

b. A cube is inscribed in a right circular cone with a radius of 1 and a height of 3. What is the volume of the cube?

c. A cylindrical hole 10 in long is drilled symmetrically through the center of a sphere. How much material is left in the sphere?

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a The longest diagonal of the cube is equal to the diameter of the sphere which is r r p 3r Thus if ... View full answer

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