a block of clay is moulded into a cube with equal side lengths of 30 cm. the clay is remoulded into a cylinder - what is the diameter of this cylinder?

Question

a block of clay is moulded into a cube with equal side lengths of 30 cm. This clay is then remoulded into a cylinder - what is the diameter of this new cylinder?

Answer 1

Volume of cube = (30)³ = 27,000 cm³

 

Volume of cylinder = πr²h = 27,000

 

  If we are going to find the diameter, some info concerning the height is required.

 

  Under the assumption that the height of the cylinder is supposed to be the same as the length of a side of the cube, then 

 

          30πr² = 27000

 

               r² = 900 / π

 

So, r = 30 / √π

 

     Diameter = 2r = 60 / √π

 

If no information related to h is given, then r² = 27000 / (πh)

 

                                                               r = 30√[30/πh)]

 

So, diameter = 2r = 60 / √[30/(πh)]