Is there a problem with this question, because the volume is in cubic centimetres and the diameter is in inches? Let's assume to start with that the diameter should have been centimetres, then the radius is 5cm. Base area * height=volume, so 25(pi)*(height)=23040. Therefore height=23040/(25(pi))=293.35cm.
If the volume had been cu in and the diameter was 10 in, the height would be 293.35 in.
To work with inches and cc, we need to convert one into the other. 10 in=10*2.54 cm=25.4 cm, so the radius is 12.7 cm. Now the base area is 161.29(pi) and the height is 23040/(161.29(pi))=45.47 cm=17.9 in.