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Planets-Are-Us has found a box company called We-Be-Cubes that only makes cubic boxes. Homework Help ✎

  1. If Planets-Are-Us wants a box that will fit the Super Jupiter piñata, which is a sphere with a radius of feet, what is the smallest box that will work? Give the dimensions and the volume.

    Find the exact volume of the sphere in ft3.

    Which positive integer, when cubed, will produce a volume bigger than that volume?

  2. We-Be-Cubes is having a clearance sale. Their Lucky box, which has a volume of cubic feet, is off! What size piñatas can fit in the Lucky box?

    If the side length of the cube is , then its volume is .

    At least how much smaller than the side length must be the radius of the piñata?

    Piñatas with radius less than  feet, or about  inches.

  3. Now the Operations Director of Planets-Are-Us needs your help! Create a formula for calculating the radius (ft) of the largest spherical piñata that a box with volume (cubic ft) can hold.

    See the hints and your personal calculations for part (b) to compile a formula.