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9-36.
  1. 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 2 feet, what is the smallest box that will work? Give the dimensions and the volume.

    2. We-Be-Cubes is having a clearance sale. Their Lucky 13 box, which has a volume of 13 cubic feet, is 50% off! What size piñatas can fit in the Lucky 13 box?

    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 v (cubic ft) can hold.

Find the exact volume of the sphere in ft3.

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

If the side length of the cube is x, then its volume is x3 = 13.

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

Piñatas with radius less than 1.18 feet, or about 14 inches.

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