Explain why the ionic radius of aluminium is smaller than its atomic radius but the atomic radius of chlorine is larger than its atomic radius.

Because Aluminum by loosing electron to form ion it's nuclear effective charge increase hance more pull to it's corresponding valence she'll thus appear smaller

While

Chlorine due to gaining of electron to form ion it's effective nuclear charge decrease thus less pull to it's corresponding valence hence appear large relatively

they are all solids.