If I had a 10Mx10M room and 5M between the floor and roof full of pennies is it worth more than 500$?

Question

I’m so confused of what to pick 🤣

Answer 1

Hi Cole,

This is a fun question. The idea is to try to multi-step problem solving and estimation.

I'm going to change the sizes and the dollar amounts so that I don't give away the exact answer to this math problem.

Let's suppose the room is 5m x 5m and that the ceiling height is 7m. If you find the volume of the room, you can find out how much space there is to put pennies in. The volume of a rectangular solid is length x width x height.

Volume of the room = 5mx5mx7m = 175m³

So what if we wanted to know if $300 worth of pennies would fit into that space. It would be useful to know how many pennies that is.

$300x100 pennies/dollar= 300,000 pennies

So now our question is whether 300,000 pennies would fit in 175m³. There are at least a couple of ways we can figure this out.

One way is to gather up a lesser number of pennies and measure or guesstimate how much volume they take up. Can you gather up some pennies in your house and put them into a rectangular container? How many pennies do you have? What is the container's volume in cubic centimeters? How many of those containers will fit inside a room with a volume of 175m³?

We can also find the volume of a single penny through online search and then figure out how much space 300,000 pennies will take up. One penny is 0.35 cm³.

How much space would 300,000 pennies take up?

300,000 x 0.35 cm³ = 105,000 cm³

We can't compare cubic meters and cubic centimeters directly. We need to convert them to the same unit. A cubic meter is 1m x 1m x 1m, which is 100cm x 100cm x 100cm, or 1,000,000 cm³.

The volume of pennies 105,000 cm³ < one cubic meter, 1,000,000 cm³

Since the pennies in this problem will fit inside of one cubic meter, they will definitely fit inside of the larger 175m³ room.

Good luck with your math work! I hope this explanation was helpful.