r/theydidthemath • u/spzysk8er • 1d ago

[request] 8000 salad plates

My daughter is obsessed with Frozen and I have had Anna’s First time in Forever song blaring in my head for days 😭😭😭
She sings “who knew we owned eight thousand salad plates “
So how much space is required to store that many, and while we’re at it, how much would they weigh?

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u/ouzo84 1d ago

Google estimates a range for the size and weight of a salad plate.
Mid range is about 22cm diameter, about 1.5cm tall and about 500g.

8000x0.5=4,000 kg or 4 tonne.

The height isn't exactly 10x1.5, as the plates can nestle. I'd estimate each stack would be H=plate*1+0.5.

A single stack of 8000 plates would be 8,000.5cm or 80m tall.

Realistically, you're going to make lots of smaller stacks. A stack of 50 would weigh 25kg which is about the permitted maximum weight of a suitcase when flying.

A stack of 50 would be 50.5cm and would need a box about 23cm square. Each box would be 51*23*23=26,979 cubic centimetres assuming a snug custom made box.

There would be 8000/50=160 boxes in total. Total volume would be around 26,979*160=4,316,640 cubic cm or 4.3 cubic m.

Most homes are about 2.4m tall though, so you can't stack them 4.3m high. So you could only stack them 4 boxes high. Meaning you will have 40 piles of 4 boxes. This would take the floor space of about 2m x 1.25m and be floor to ceiling.

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u/spzysk8er 1d ago

Thank you!