Subject: Volume of a Cube?
Name: Greg
Who are you: Parent (All)

My son who is in grade 8, brought home the following question and asked for my help in solving it. Can you please show me, how to show him?

"Nicolai said that 6 billion can represent the volume of a cube. How many units long is the cube? How do you know?"

Thank you,

Hi Greg.

A cube is a shape that the length = width = depth. To calculate the volume, you multiply these together, so if L is the length (and therefore the width and depth), the volume is L x L x L, or L3.

To go from the volume to the length, you take the cube-root of the number. The cube root of 6 billion is hard to do without a calculator, but I can give you this approximation:

Since 6 billion = 6 x 1 000 x 1 000 x 1 000, then the cube root of 6 billion is 1 000 times the cube root of 6. That's easier to solve. The cube root of six is a little less than 2 (because 2x2x2 is 8 - too much). So the answer is a bit less than 2000.

6 billion is about the number of people living now on Earth. If you gave each person a box that was 1 meter by 1 meter by 1 meter to sit in and then stacked them into a big cube, you'd have all the people in the world sitting in boxes in a space that is a bit less than 2 km by 2 km by 2 km!

Stephen La Rocque.>

PS: (I finally found a calculator and it says the cube root of 6 is about 1.817, so the cube root of 6 billion is one thousand times that.)