  ### Home > INT3 > Chapter 9 > Lesson 9.1.3 > Problem9-36

9-36.

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

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.

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 $13$ box, which has a volume of $13$ cubic feet, is $50\%$ off! What size piñatas can fit in the Lucky $13$ box?

If the side length of the cube is $x$, then its volume is $x^{3} = 13$.

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.

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.

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