Billions of Boxes of Air

Here's your nightly math! Just 5 quick minutes of number fun for kids and parents at home. Read a cool fun fact, followed by math riddles at different levels so everyone can jump in. Your kids will love you for it.

Billions of Boxes of Air

June 22, 2016

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?




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.

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About the Author

Laura Overdeck

Laura Overdeck

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking while still in diapers, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.

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