Now that it’s summer, lots of people are thinking about going to the beach. So our fan Sophia Y. asked, how many sand particles would it take to cover a person? First, there’s a grown-up formula to figure out how much area your skin covers! (you multiply your weight and height by other numbers, to start). We tried it for a regular-sized 6-year-old (50 pounds, 42 inches tall), and got 8 ½ square feet of skin area. A medium-sized grown-up woman has about 18 square feet, and a man has more than 20 sq ft. Each grain is 1/1,000th of a foot wide, so it takes 1,000 x 1,000 or about 1 million grains of sand to cover just 1 square foot. That’s just a thin layer of single grains…if you want a few inches of sand, you need hundreds of layers, giving us over a billion grains for a grown-up! Luckily the beach has plenty of sand for the job.
Wee ones: If your body has 7 square feet of skin and your friend has 5 square feet, who needs more sand to be totally covered?
Little kids: If your whole body has 8 square feet of skin, and each arm takes up 1 square foot of that and each leg takes up 2 square feet, what does that leave for your torso (the part in the middle)? Bonus: How much more area would you need to reach 10 square feet?
Big kids: If you dig out 20 cubic feet of sand (imagine perfect cubes 1 foot wide), then shovel 8 cubic feet back into the hole, then dig out 4 cubic feet, then dump 1 cubic foot back in…how many cubic feet have you dug out in total? Bonus: If you now make the hole twice as wide and twice as long (with same depth), how much sand have you dug out in total? (Hint if needed: What if you made it just twice as wide?)
The sky’s the limit: If you’re covering a teenager with 16 square feet of skin total 3 inches deep in sand, how many billions of grains do you need — and how do you write that in digits? (Remember, the area facing up is just half of that, and you need 1 billion grains for each cubic foot (12 inches deep)).
Wee ones: You have more.
Little kids: 2 square feet, since your arms and legs take up 6. Bonus: 2 more square feet.
Big kids: 15 cubic feet. Bonus: 60 cubic feet. It would be just 30 cubic feet if you doubled in only one direction.
The sky’s the limit: 2,000,000,000 grains of sand (2 billion). You’re covering just 8 square feet of skin, and if you went 1 foot deep, you would need 8 billion grains. But 3 inches is only 1/4 as deep, so you need only 1/4 as many grains as that.
And one helpful tip for the beach: if you’re covered in wet sand, just rub talcum powder into it. The powder soaks up the water making the sand stick, and it will all fall off!
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 before she could walk, 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.