Today from Bedtime Math: Billions of Boxes of Air

We can't see it, but all around us is air. But air isn't everywhere -- in outer space there's nothing at all, which is a "vacuum" (if you went in outer space without an astronaut suit, your whole body would explode!). Earth has air for only a few miles above ground, called our "atmosphere." So our fan Rylan N. asked, how much air does Earth have? Well, about 3/4 of our air by weight is stuffed into the first 6 miles above ground. So we can take Earth with that blanket of 6 miles of air, making a ball 12 miles wider, find its volume, and then subtract the volume taken up by Earth itself. Earth is about 7,926 miles wide, so the 7,938-mile wide ball (12 miles wider) minus the 7,926-mile wide ball gives us more than 1 billion cubic miles of air! Imagine a box 1 mile wide in every direction, filled with air...we have 1 billion of them. That air weighs about 11 quintillion pounds, which is an 11 followed by 18 zeros. Plenty for all 8 billion of us humans, as long as we keep it clean!

Wee ones: If you breathe in, then out, then in, then out...what comes next?

Little kids: A 6-year-old's lungs can hold about 1/2 gallon of air, and a 14-year-old's hold about 1 gallon. How many years does the 6-year-old have to wait to hold a full gallon? Bonus: If the 6 year-old takes in 5 full breaths and the 14-year-old takes in 5, who breathed in more air?

Big kids: If you fly in a plane 30,000 feet up, are you above or below the 6-mile mark for the thick part of our atmosphere? (Reminder if needed: A mile has 5,280 feet). Bonus: Can you "spell" 1 billion as a number?

Answers:

Wee ones: You breathe in.

Little kids: 8 more years. Bonus: The 14-year-old, since it's the same number of breaths but bigger.

Big kids: Below 6 miles...a mile would have to have just 5,000 feet for it to match. Bonus:1,000,000,000.