Solution:

Given data:
- Side of aluminum cube = 10 cm
- Volume shrinkage of aluminum during solidification = 6%
- Height of cylindrical riser = Diameter of cylindrical riser

To solve this problem, we need to find two things:
1. Shrinkage volume of aluminum cube on solidification
2. Minimum size of the riser so that it can compensate for the shrinkage of the aluminum cube

Calculating Shrinkage Volume of Aluminum Cube:

- Volume of aluminum cube = (Side)^3 = 10^3 = 1000 cm^3
- Shrinkage volume of aluminum cube on solidification = 6% of Volume of aluminum cube
= 6/100 * 1000 = 60 cm^3

So, the shrinkage volume of aluminum cube on solidification is 60 cm^3.

Calculating Minimum Size of the Riser:

- The riser is used to compensate for the shrinkage of the aluminum cube during solidification.
- The volume of the riser should be equal to the shrinkage volume of the aluminum cube.
- Volume of cylindrical riser = πr^2h
- Diameter of cylindrical riser = h (given)
- So, Volume of cylindrical riser = πr^2h = π(d/2)^2h = π(h/2)^2h = (π/4)h^3
- Volume of cylindrical riser should be equal to Shrinkage volume of aluminum cube
- (π/4)h^3 = 60
- h^3 = (4/π)60
- h = (4/π*60)^(1/3)
- h ≈ 6.4 cm

So, the minimum size of the riser should be approximately 6.4 cm.

Explanation:

- While casting an aluminum cube, there is a possibility of shrinkage during solidification.
- To compensate for the shrinkage, a riser is used which will provide additional molten metal to the casting until solidification is complete.
- The volume of the riser should be equal to the shrinkage volume of the aluminum cube.
- So, we need to calculate the shrinkage volume of the aluminum cube and then find the minimum size of the riser which can compensate for the shrinkage.
- In this problem, we have calculated the shrinkage volume of the aluminum cube by using the given shrinkage percentage.
- Then, we have calculated the volume of the cylindrical riser and equated it to the shrinkage volume of the aluminum cube to find the minimum size of the riser.
- Therefore, the minimum size of the riser should be approximately 6.4 cm to compensate for the shrinkage of the aluminum cube during solidification.