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.)
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!
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.
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.
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.