One the side of the pail near the bottom... cut or drill a hole large enough so that the cord's pronged end can pass through it.
Then coil the rest of the cord into the bucket.
Now... when you're ready to use the extension cord... it will pull out smoothly and easily to go wherever you need it to.
You can plug the ends of the cord together to keep from dragging the end that comes out the bottom of the pail... and in the center of the coil... you cancarry tools to your next project site.
And make sure you empty the pail after every use... and store it where a small child can't get to it. It's not unheard of for a child to crawl into a pail this size and get stuck and suffocate... or even drown... if it's filled with liquid.