Question

A box 1 m by 5 m is filled with cubes of volume 1 cm3. If these small cubes were stacked one on top of the other, how many kilometers high would stack be?

Answer 1

The stack of small cubes would be 100 kilometers high.

Imagine a box measuring 1 meter by 2 meters by 5 meters, filled with tiny cubes, each measuring just 1 cubic centimeter. How high would the stack be if we lined all these little cubes up, one on top of the other?

First, let's calculate the total number of cubes. The box's volume is 10 cubic meters, and since each cube is 1 cubic centimeter, we have 10,000,000 tiny cubes crammed inside.

Now, let's imagine stacking these cubes vertically. Each cube contributes 1 centimeter to the height. So, the total height of the stack would be 10,000,000 centimeters.

But how does that translate to kilometers? Remember, 1 kilometer equals 100,000 centimeters. Therefore, our stack of tiny cubes would reach a staggering **100 kilometers** high!

That's right, a stack of these tiny cubes, once lined up vertically, would soar 100 kilometers above the ground, reaching into the stratosphere! It's a mind-boggling thought, highlighting the power of sheer quantity.

Answer 2

THe answer is that the height would be 10 km

To solve this, we first need to find the volume of the box. Then calculate how many amll cubes of 1mm there are inside, and then calculate the height of them stacked.

For the first part:

The volume of a rectangular prism (or box) is calculated multiplying each side with each other. In this case we have a side of 1m , a side of 2m and a side of 5m. Then:

`V=1m\cdot2m\cdot5m=10m^3`

Now to know how many cm^3 there is in the box, we know that each m3 is one million cm3. This is:

Now we have 10m3. Thus:

If we stack them, in vertical, then each smal cube will count as a cm. Then we want to calculate, how many kilometers are 10,000,000 cm.

Since 1 meter = 100 cm:

Finally, 1 kilometer = 1000 meters: