Will this pet house fit inside the enclosure with the wheel still in there?

How to say “Will this pet house fit inside the enclosure with the wheel still in there?” in Japanese

In Japanese

回(まわ)し車(ぐるま)を置(お)いたままでも、この隠(かく)れ家(が)はケージに入(はい)るかな？

Mawashiguruma o oita mama demo, kono kakurega wa kēji ni hairu ka na?

Will this pet house fit inside the enclosure with the wheel still in there? in other languages