A friend sent me a link to this giant beach ball on Amazon. It is 12’ in diameter! The reviews are hilarious because they’re mostly about it rolling out of control and flattening everything in its way. We got to wondering just how much it weighs when inflated but I suck at math and wouldn’t even know where to start figuring it out.
Any math geniuses out there?
PS Yes I do want one!
Not a scientist, but if it’s inflated just enough to hold it’s shape, I’d say it weighs the same as it does un-inflated.
The weight of the additional air needed to make it “bouncy” would of course depend on the air pressure inside.
The volume of a 12’ diameter sphere is about 905 cubic feet (if I didn’t drop a zero anywhere.
Looked at the link:
GIGANTIC: Measuring 12 feet from pole to pole, we’re pretty sure this puts other “jumbo” beach balls to shame
CLASSIC: With an astounding 659,000 cubic inch volume, it’s just like a classic beach ball, only gianter "
I don’t think the diameter is 12’ but they appear to be measuring along the circumference.
A 12’ diameter gives 905 cu ft while their 659,000 cu inch measure is only 381 cu ft.
Now that you mention it, the man standing next to it should be around half its height if it really is 12’. So it looks more like its really 8-9’ in diameter.
That’s dissappointing but now I have a followup question, can you figure out the real diameter from the “pole to pole” size?
At least 30 lbs (14 kilos).
Thank you! 
Gravity won’t be pulling down on it any harder - the weight won’t be any different inflated than uninflated - but the whole assembly of plastic and air will have more total mass than just the plastic, and that will matter when the moving ball slams into things.
12 feet is 3.65 meters, so I get a volume of 25.6 cubic meters. Air density is about 1.2 kg/m^3, so I get 30.7 kilograms, or 68 pounds. So if this moving beach ball hits an object, that object will be dealing with a 68-pound air mass + ??? pounds of plastic.
There is also the added mass effect: for objects moving through a fluid, they drag some of the ambient fluid with them. When the object accelerates/decelerates, that extra mass of ambient fluid must also be accelerated/decelerated. The amount depends on the properties of the fluid and the shape of the object. It’s an effect that matters for large marine vessels, and also for this beach ball: that Wikipedia page says the added mass for a spherical body is 1/2 the volume times the density of the fluid. So really, a bystander caught off-guard and struck by an errant 12-foot beach ball would be dealing with the inertial effects of a 100-pound object (this does not include the weight of the plastic itself). Hope it’s not inflated too firm.
That’s like half a cubic foot of solid vinyl? So 40-50 lbs? Not counting any air…
I was wondering how long it would take to blow it up “manually”.
Assuming a complete emptying of the lungs on each breath (average of 6 litres or 365 cubic inches), the 659,000 cubic inches would take roughly 1,800 full breaths.
I think the vinyl would probably be about 10 lbs or so.
That’s the mass of air without buoyancy.
Imagine a water balloon filled with water. If you weigh it under water, it will have only the Small weight of the rubber balloon itself.
Maybe they’re measuring the way Spinal Tap did for Stonehenge.
Do you want the total weight or the buoyant weight?
Maybe I should start a poll instead of asking here, but I always find it confusing when people say they are bad at math and then ask a question that is basically just multiplying two numbers together on your phone. What part of that process is confusing? Or is it just like “oh no, math!” and the panic shuts down any further thought? And if the latter, was there like a childhood trauma in math class?
OK, 12 feet “pole to pole” means half the circumference, or a circumference of 24 feet.
24/3.14= 7.6 feet diameter. Or, 91.2 inches. So R=45.6 inches, which gives a volume of 397,176 cubic inches.
But the ad states a volume of 659,000 cubic inches. [doing some math…] This calculates to a radius of 54 inches, or a diameter of [more math…] 9 feet.
So, either their calculations are in error, the ball is not spherical, or their “pole to pole” measurement is not truly “pole to pole”.
Because I don’t know what two numbers to multiply. Other people managed to answer without being rude. You didn’t have to answer at all.
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Y’know, your name doesn’t entitle you to make snarky remarks at other posters. This post is completely jerkish, and contributes absolutely nothing to the thread. I’m instructing you to refrain from these kinds of remarks in General Questions. Doing so will be subject to a warning.
Colibri
General Questions Moderator
That wasn’t meant to be snarky, it’s an actual question I’m curious about. Legitimately don’t understand.
Moderating
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Colibri
General Questions Moderator
When I had geometry class Reagan was president.
I know I could have looked up the formulas and density of air and stuff and come up with an answer but I wouldn’t know if it was the right answer
I thought it would be a fun thread and give everyone a break from the coronavirus - rioting - politics threads
Thank you to the folks who bothered trying to figure it out and to Colibri for your intervention.
Thank you for your response.
Are you interested in the buoyant weight (the number a scale will read) or the total weight (the force of gravity on the mass of the object)?