Our Earth is really, really big, at least compared to us. It’s a ball that measures 25 *thousand* miles all the way around. So our fan Sophia H. asked, how many cheeseburgers could we fit inside Earth if it were hollow? 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 cheeseburgers, we could count the burger as a 4-inch wide ball, and we know Earth is an 8,000-*mile* wide ball…let’s do the math to find out how many can fit!

*Wee ones:* What shape is Earth?

*Little kids: *If you stack 8 cheeseburgers, then eat 1, how many do you have left? *Bonus: *How many 4-inch cheeseburgers do you have to line up in a row to make 1 foot (12 inches)?

*Big kids: *If 1 ball holds 27 times as much space (volume) as a 2nd ball, how many times as wide as the smaller ball is the bigger ball? (*Hint if needed:* What number times itself times itself makes 27? Very few numbers divide into it!) * Bonus: *How many 4-inch ball-shaped burgers can fit inside a 16-inch wide ball? (Don’t worry about gaps between them – assume they can squish and change shape to fill all space.)

Answers:

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

*Little kids:* 7. *Bonus: *3 cheeseburgers, since 4 + 4+ 4 = 12.

*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.

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.