There are 750 toothpicks in a regular sized box. If a jumbo box is made by doubling all the dimensions of the regular sized box, how many toothpicks will the jumbo box hold?
I'm not sure if I am right but I think the answer is 1500.
The volume of the jumbo box will go up by: 2^3 = 8 times. Therefore, it should hold:
8 x 750 =6,000 toothpicks.
Because when you double the dimensions of the box, the volume goes up as cube or 3rd power of the dimensions. So, assume that the dimensions of the small box were: 1, 2, 3 inches. Then the volume would be: 1 x 2 x 3 = 6 in^3. Now, suppose you double the dimensions of the jumbo box to: 2, 4, 6. Then the new volume of the jumbo box would be: 2 x 4 x 6 = 48 in^3. So now, you divide the volume of the jumbo box by the volume of the regular box and you get: 48 / 6 = 8 times larger than the smaller box. Do you see it now?.