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 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:

$1m^3=1,000,000\operatorname{cm}^3$

Now we have 10m3. Thus:

$1m^3\cdot10=10,000,000\operatorname{cm}$

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:

$\frac{10,000,000\operatorname{cm}}{100}=10,000m$

Finally, 1 kilometer = 1000 meters:

$\frac{10,000m}{1,000}=10\operatorname{km}$