I desperately need someone to look over my calculations

My High School is pretty proud of it's tradition and I plan on pulling a little pride and tradition of my own this year.

there is a courtyard type area in our school. the top is ground level and it is depressed into the earth with stairs down to the bottom. if it were to have a cross section, it would look something like this. it is a cylinder cut in half from top to bottom.

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each step is 6" high and 32" long. the courtyard has 2 radii, one is 440", the other is 540".

I need to know the volume of the courtyard so i cut it up into 6" high cylinders with pi(AB)*H instead of pi(r*r)*h

the base cylinder = ((540"-(6"x 6steps))x(440"-(6"x 6steps))x 6" x pi) / 2 = 258912pi in. cubed

((540"-(6"x 5steps))x(440"-(6"x 5steps))x 6" x pi) / 2 = 319200pi in. cubed

((540"-(6"x 4steps))x(440"-(6"x 4steps))x 6" x pi) / 2 = 385632pi in. cubed

((540"-(6"x 3steps))x(440"-(6"x 3steps))x 6" x pi) / 2 = 458208pi in. cubed

((540"-(6"x 2steps))x(440"-(6"x 2steps))x 6" x pi) / 2 = 536928pi in. cubed

((540"-(6"x 1steps))x(440"-(6"x 1steps))x 6" x pi) / 2 = 621792pi in. cubed

((540"-(6"x 0steps))x(440"-(6"x 0steps))x 6" x pi) / 2 = 712800pi in. cubed

I did this for each of the steps to get a total area of 3,293,472pi in cubed

I then took this and divided it by the number of in. cubed in 1 ft cubed

3293472pi x 1'/(12"x12"x12") = 1905.95pi ft cubed

so that is 5987.7 ft cubed.


My plan is to fill the area with balloons which are school colors. What I need to do is to use this volume to find the number of balloons I have to use to fill the area. The volume of a sphere is 4/3pi x r cubed. Various balloon sizes i have found are 9, 12, and 16 inch diameter, so 4.5, 6, and 8inch radii.

How would I find the number of spheres that will fit in a cylinder? this is my main problem right now

I'm not entirely sure whats going on, but:

Balloons have what we in the business call 'compliances'.

Doesn't matter if you're out slightly, push a little harder and it will fit.

i too am unsure of what you are saying, but if you want to find the amount of balloons you can fit into a set volume:

get a large cardboard box, blow up some balloons. more than you need to fill them up. now randomly throw balloons into the box until its with the rim, or just over. count the number of balloons in them. do this about 10 times, the more the better. Now find the average of those numbers. Then calculate the volume of the box and then work out the average density of balloons per unit volume. then apply it to your calculations


the reason you want to do this is because balloons arent spheres, and they often arrange themselves in random fashions because of this weird shape and because the friction of rubber on rubber stops them from arranging themselves in the most efficient manner. in the real prank, the balloons will arrange themselves just as randomly, so you need to repeat the test several times so you get a good average, and because the courtyard is relatively large compared to the box, it should have a really similar density of balloons.

now in the real test, you will need to overcompensate. balloons will be popped , stepped on or blown away. you might also accidentally not have enough, so its good to bring a bit more

I actually see whats happening. The formula is correct (but I didn't check if the actual calculations where) if you where filling it with liquid. but as it is balloons will occupy much more space then they will contain. so if I where you I would only calculate the smallest circle to ground level and what would probably be sufficent.

Just get a shitload of baloons. If you don't have enough, get more. If you have extra, find something elso to do with them, or just save them for later.

i too am unsure of what you are saying, but if you want to find the amount of balloons you can fit into a set volume:

get a large cardboard box, blow up some balloons. more than you need to fill them up. now randomly throw balloons into the box until its with the rim, or just over. count the number of balloons in them. do this about 10 times, the more the better. Now find the average of those numbers. Then calculate the volume of the box and then work out the average density of balloons per unit volume. then apply it to your calculations


the reason you want to do this is because balloons arent spheres, and they often arrange themselves in random fashions because of this weird shape and because the friction of rubber on rubber stops them from arranging themselves in the most efficient manner. in the real prank, the balloons will arrange themselves just as randomly, so you need to repeat the test several times so you get a good average, and because the courtyard is relatively large compared to the box, it should have a really similar density of balloons.

now in the real test, you will need to overcompensate. balloons will be popped , stepped on or blown away. you might also accidentally not have enough, so its good to bring a bit more

thanks man, thats a pretty good idea that I hadn't thought of. I'll probably get on that in the next few days. I think what's gonna end up happening is we're gonna need close to 6000 balloons regardless

oh, and take pics/vids. I want to see how this turns out. My epic sense is tingling.

For the roomates birthday the other week i blew up over 100 balloons and left them all round the house. It was a fun night.

oh, and take pics/vids. I want to see how this turns out. My epic sense is tingling.

Oh yeah dude, fersure. I'm good friends with a couple of the year book girls, and I'm gonna see if they want to come and help take vids and/or pics. Hopefully people can keep their mouths shut about this until the senior slideshow at the end of the year. either way we're gonna make some shirts that have some phrase on em like "One last blowout" or something to do with balloons

Dont forget a balloon isnt a sphere, more pear shaped.

Just measure how big one is cubed, then figure out how many per cubic meter, then add a few.

you could find the average volume of one balloon, find the volume of one stair, and the volume of the cylinder integrate the total volume of the stairs ofver the interval of zero to the top, subtract that from the volume of the cylinder and the divide the volume of the cylender by the volume of the balloon, and fill that many ballons,, you might want to take a wide average of the baloon volumes however. nad if you could find the volume that is lost based on the curvature of the baloon, so find the formula for the curve(or approximate it) rotate it around the x axis and viola, subtract that from the total volume of balloons , and you should be able to calculate the number of balloons.

http://www.chiliahedron.com/ballroom/

For quick cleanup, fill the balloons with propane.

Just get a shitload of baloons. If you don't have enough, get more. If you have extra, find something elso to do with them, or just save them for later.

The answer is, as bobfish pointed out, a shitload.

one thing,, how the hell is this considered a prank?