Knitting a sweater pattern - cast on sleeves

I am knitting a sweater pattern. The first step is to knit the back part of the sweater. I am almost done with this step and the next step is calling for cast on sleeves. It starts by saying to cast on x number of stitches. My question is the knitting needle I am using is a US 9 and it is about 10" long. I am not sure if I am supposed to move to another longer needle or how am I suppose to cast on the sleeves. In the materials section, it doesn’t say anything about another set of needles or what other tools to use. It does say that after casting on the sleeves I will have a lot more stitches then when I first started the back part of the sweater. I need help understanding how to do this.