What size grocery bag would I need to hold Avagadro's Number of carrots?

Question

Explain how you found the answer.

Answer 1

6.022 * 10^23 carrots. Lets use the small peeled and ready to eat kind (I hate to scrape). If each carrot has an average packing volume of 16.61 cubic centimeters, then the total volume would be

16.61 cc * 6.022 * 10^23 = 1.00 * 10^25 cc or about 1.00 * 10^22 Liters or about 1.00 * 10^19 cubic meters (or about 10^10 cubic kilometers).

By the way, the volume of the planet Earth is 1.0832×10^21 m3, so this is about 1/10 of the Earth. If you used the big bunch carrots, you would need a shopping bag as big as the Earth to hold them.

Answer 2

Make an assumption - for example 10 carrots fit into 1 litre.
10,000 carrots will therefore fit into 1 cubic metre.

Now multiply the 1 cubic metre by Avogadro's number divided by 10,000. Then divide by 1 million to get cubic kilometres. You have still got a vast volume! Try comparing your answer with, say, the Atlantic Ocean.