Mathematical question (diameters)

[The Gauge]

Anyone good at math(s) that can calculate a diameter at a given point?

I want to purchase some plastic plant pots to sit inside some terracotta pots on my patio, that way I can lift plants out when they die back and slot another pot inside containing different plants, maintaining the planting throughout the seasons.

With the plastic plant pot sketched below, because of the shape of the terracotta pots I'd like to know the diameter of the plastic plant pot at a certain point, being 20cm down from the top.

I guess I can calculate the diameter half way down the pot by calculating the difference between the top & bottom diameters, then halving that figure then adding it back on? But what about the diameter at any other given point?

Is there a formula I can use to get the same measurement with different sized pots where I have their measurements but wish to know the diameter at certain points down from the top?

So the pot I'm thinking of buying is..

320mm diameter at the top
235mm diameter at the base
260mm tall

[The Gauge]

The reason I ask is because the inside of the terracotta pots have a ledge part way down the inside and I need to know if the plastic insert pots will clear it or foul on it etc..

[The Gauge]

I must say I am very disappointed with the responses. I was hoping for much head scratching and pages of bickering over the correct answer, with folk insulting each others intelligence and falling out with each other, and comments such as 'if you don't know the answer then perhaps you shouldn't be gardening' etc

I've measured the diameter inside of the terracotta pots where the ledge is, and its 255mm, exactly the same as the plastic plant pots at the same point, so at least I know they will fit nicely. As for those who were able to calculate the correct answer, a big thank you and have you considered being a contestant on programmes such as Krypton Factor or Mastermind. If not you are underselling yourselves

And thank you to JohnWest for conducting your CAD experiment, and for the cans of divine tuna.

Edited by The Gauge on Thursday 9th May 14:16

[The Gauge]

Final question...

For the next size up pot, what would the diameter be at the same point please?

[The Gauge]

I must say I am very disappointed with the responses. I was hoping for much head scratching and pages of bickering over the correct answer, with folk insulting each others intelligence and falling out with each other, and comments such as 'if you don't know the answer then perhaps you shouldn't be gardening' etc

pti said:

Give a man the answer, he'll survive for a few hours.

Teach a man the calculation and he'll still ask for the fking answer...

GroundEffect said:

Username checks out.

This really isn't hard. It's not even GCSE level.

Seems I spoke too soon

Edited by The Gauge on Thursday 9th May 16:41

[The Gauge]

RustyMX5 said:

If you're planning to take the plastic pots out if the plants die, are you taking the expansion of the plastic into account in the hot summer sun?

I'll be removing them when flowers (such as spring bulbs) have finished flowering, and elsewhere in the garden out of sight I'll be growing other plants in the pots to replace them, so will be rotating them through the year. I do this already but I've bought new terracotta pots so need to replace the plastic inner pots to fit.

Good point about expansion though, but they should'nt be in contact with the inner walls of the terracotta pots other than maybe where the ledge is.

[The Gauge]

Sheepshanks said:

The plastic pot should be pretty reliably the same, but I wouldn't rely on the terracotta pots always being spot-on, unless you can try before you buy. A bit of clearance would be handy.

I've already bought the terracotta pots so the measurements are what I have taken. The plastic inner pots wont be as tall but I'll be standing them on bricks inside the terracotta pots.

[The Gauge]

JohnWest said:

Sorry for the late reply folks, it turned out to be quite a busy day and I had to use CAD to design stuff!

Anyway, onto important matters. As hidetheelephants said, the answer is 298 but I feel the PH collective (well, maybe just Matty) would be disappointed if I didn't model it in CAD. So just in case you needed a your answer to more than 1 d.p., the diameter is 298.2758621mm.

Not quite the accuracy I expected but I guess that’ll have to do
Many thanks for taking the time