An Apple a Day Fills the Plane

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.

An Apple a Day Fills the Plane

June 18, 2016

Have you ever taken a plane ride? It’s usually at least an hour trip, so the airplanes give us little snacks – but it’s never enough. Maybe that’s why our fan Tristam J. asked, how many apples could you fit inside an airplane? Well, you have to find the space, or “volume”, that 1 apple fills, then find the volume of the plane. If the apples were perfect balls, or “spheres”, and you packed them as tightly as you could, they’d have gaps between them…the balls would take up about 3/4 of the total air space. Now, an apple that’s 2 inches from the peel to the middle takes up 4/3 times pi (3.14) times 2 times 2 times 2 again. That’s 33 cubic inches, or little cubes that are 1 inch wide in every direction. But that’s only ¾ of the air the apple fills if stacked…it actually takes up 44 cubic inches. Thankfully, someone already figured out that a 747 jet has about 1,000 cubic meters of space for both passengers and suitcases, or about 35,000 cubic feet…or about 61,000,000 cubic inches. Dividing by 44 cubic inches per apple, you can fit about 1,386,000 (1 million 386 thousand) apples in there. You could eat all of them, or you could carve one into an airplane, like Tristam did!

Wee ones: Do you see any balls in the room around you? Are they bigger or smaller than an apple?

Little kids: If you put an apple on the table with 6 apples around it, how many do you have in total?  Bonus: When you pack another layer on top and below, the apple gets another 3 above and 3 below. Now how many does the center apple touch? (Remember not to add in that center apple itself!)

Big kids: If the plane can hold 1,386,000 apples, how many people could you feed apples if each one wants 1,000 of them?  Bonus: What if each person just wants 100 — now how many people can you feed?

 

 

 

Answers:
Wee ones: Different for everyone…see how many you find, and how big they are!

Little kids: 7 in total.  Bonus: 12 apples, because it touches the first 6 plus 3 plus 3.

Big kids: 1,386 people.  Bonus: 13,860 people.

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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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