Volume · Superchallenge problem

An empty tank is shaped like a box $50$ cm long, $40$ cm wide and $40$ cm tall. A tap pours in $5$ liters of water every minute, and at the same time a drain lets out $2$ liters every minute. After $10$ minutes the drain is closed, and the tap keeps running. How many minutes after the start is the tank completely full? (One liter is $1000$ cubic cm.)