2. CBQ - Perfect cubes II

A group of students from Class \(8\) is helping their school’s handicraft club prepare wooden cube-shaped crates for an exhibition. Each crate must have a volume that is a perfect cube, because the crates are to be stacked neatly without leaving gaps.

 

1. Find the smallest number by which 6750 must be divided so that the quotient becomes a perfect cube.

 

2. Find the smallest number by which 18225 should be multiplied to make it a perfect cube.

 

3. Which whole number cubed gives a value closest to 30000 but not exceeding it?

 

4. If the total number of blocks used is 9261, then find the side length.