How Many Snacks Can We Stuff Inside Earth?

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.

How Many Snacks Can We Stuff Inside Earth?

May 12, 2016

Our Earth is really, really big, at least compared to us. Think of it this way: when you look out over the ocean or a flat field, that faraway spot where sky meets ground is about 12 miles from you, out of 25 thousand miles all the way around Earth. So fans have asked how much stuff we could fit inside Earth if it were hollow. Cynthia D. wants to know how many pizzas we could fit inside our planet, and Sophia H. asked, how many cheeseburgers? Balls work a lot like cubes: if a cube is 2 times as wide as another, the bigger cube holds 2 x 2 x 2 or 8 times as much space. If it’s 10 times as big, it holds 10 x 10 x 10, or 1,000 as much volume. Balls work the same way. As for filling Earth with food, a stack of 16-inch pizzas could count as an 16-inch ball, and a cheeseburger as a 4-inch ball. And Earth is an 8,000-mile ball. Let’s do the math to find out how many snacks can fit!

Wee ones: What shape is Earth?

Little kids: If you stack 8 pizzas, then eat 1, how many do you have left in your “ball” of pizza?  Bonus: How many 4-inch cheeseburgers do you have to line up to be wider than an 18-inch pizza?

Big kids: If 1 ball holds 27 of another ball, how many times as wide is the bigger ball? (Hint if needed: What number times itself times itself makes 27? Very few numbers divide into it!)  Bonus: If you stack 16-inch pizzas to make a 16-inch ball, how many 4-inch ball-shaped sliders can fit inside the same space? (Don’t worry about gaps between them – assume they can squish and change shape to fill all space.)

The sky’s the limit: If a mile is about 10,000 times as wide as a very big (1/2-foot) cheeseburger, and Earth is 8,000 times as wide as that burger ball, about how many burgers fit inside Earth? These are bigger numbers than our usual, but if you track all those zeroes on paper, you can give it a try!

 

 

 

Answers:
Wee ones: A circle from the side, and in 3D, a “sphere.”

Little kids: 7 pizzas.  Bonus: 5 of them, since 4 of them will span only 16 inches.

Big kids: 3 times as wide, because 3 x 3 x 3 = 27.  Bonus: 64, because you can fit 4 x 4 x 4 as many.

The sky’s the limit: 512,000,000,000,000,000,000,000, or 512 million million billions (which is a sextillion). For starters, you can fit 10,000 x 10,000 x 10,000 or 1,000,000,000,000 (1 trillion) cheeseburgers in each mile-wide ball. Then, you can fit 8,000 x 8,000 x 8,000 or 512,000,000,000 (512 billion) mile balls inside Earth. Each of those has 1 trillion cheeseburgers, so then you multiply those two huge numbers. If we wanted then to figure out pizza, a 16-inch stack of pizzs is as wide as 2 2/3 of these bigger burgers. Then, 2 2/3 x 2 2/3 x 2 2/3 equals about 19 cheeseburgers taking the same space as each stack of pizzas. So if we divide by 19 we get 27,000,000,000,000,000,000,000 stacks of pizza. And if each stack has 10 pizzas, we get 270,000,000,000,000,000,000,000 pizzas!

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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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