you have two containers. one is a cylinder with a height of 15 inches and a diameter of 10 inches. the other side is a cube with sides of 12 inches.
what is the volume of the cylinder? what is the volume of the cube?

- anonymous

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- anonymous

volume of a cylendar = pi r^2 h. cube is length times width times depth

- anonymous

so the volume of the cylinder would be 1177.5 inches^3

- anonymous

i get 1178.09, lemme try it again though

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- anonymous

well for pie i just use the first 3 numbers.. 3.14

- anonymous

ahh, yup that will do it

- anonymous

and the cube would be 12*12=144

- anonymous

that would only be the surface area of one side of the cube, its 12^3 height, width, and depth

- anonymous

so 1728inches^3

- anonymous

you got it

- anonymous

one more question: how many gallons of water are needed to fill the cylinder? (hint: 1 gallon of water is .1337ft^3)

- anonymous

if you know one gallon takes up .1337 ft cubed, and the cyl has 1177 ft cubed of space then some division will get you how many gallons per cyl

- anonymous

and are you sure its .1337 per gallon? that seems kinda small considering a gallon of milk is roughly a cubic foot in real life

- anonymous

that means you'd need 10 gallons to fill one cubic foot, just seems big to me but maybe im wrong?

- anonymous

oooooh we are dealing in inches here. your .1137 ft needs to be converted to inches (easy, 12 inches per foot) to get you cubic inches or you can go the other way anf find out how many cubic feet the cyl has and then do your division. gotta make sure the scales are correct and then its simple division

- anonymous

i cant convert worth crap i dont understand converting

- anonymous

okay, if you have 12 inches per foot, theres 24 inches in 2 feet (12*2), theres 36 inches in 3 feet (12*3). so that also means you could take some random number of inches, lets pick 247 (totally random) and we know that 20.5833 feet is the same as 247 inches. (247/12). do you see how it works?

- anonymous

multiplying and dividing are really just the same thing, one is forward and one is backwards. division tells you how many of A is in B. multiplying tells you if you had A number of groups and B number of items per group, what is the total number of items

- anonymous

ok

- anonymous

so i would do 1177.5*12

- anonymous

almost, conversion of cubic numbers is a bit more trickey. you can either convert before finding the answer in ^3 or if you do it afterward you need to remember that your dealing with a volume in 3 dimensions. because think about the physical shape of a cubic foot (a box that is a ft by ft by ft) now think about 12 1 inch cubes (little bigger than 12 dice) not quite the same size as eachother. thats because your forgetting a whole dimensions

- anonymous

however, if you know taht there are 1728 cubic inches per cubic foot (thats a true statement btw) then you can do your one to one conversions

- anonymous

ok

- anonymous

does that make sense?

- anonymous

kinda

- anonymous

well to get that 1728 number all you are doing is saying, i have 12 units up, 12 units deep and 12 units wide.

- anonymous

ok

- anonymous

so if you wanted to convert 4 cubic feet it would just be how many inches in one cubic foot times 4, aka 1728 times 4

- anonymous

1177.5*4=4710

- anonymous

sorry no, its not times 4 because that would be a 2X2X2 ft square. to find for a 4ft cubed would be 4*12=48 48^3=110592

- anonymous

i meant to say 64 not 4 because it expands exponentially ie: 4^3 is what you multiply by (4^3=64)

- anonymous

haha now i went and confused you more by typo-ing. im sorry about that. you have to remember that the number your multiplying by is cubed as well.

- anonymous

im already confused

- anonymous

its that 1728 number (how many cubic inches in a cubic foot) times how many cubic feet your finding ^3 example: 3 cubic feet has 1728*3^3 cubic inches in it. 24 cubic feet has 1728*24^3 cubic inches in it

- anonymous

what i was saying before is you can figure it out by converting first if you want. so your 3 cubic feet has 3 feet in each direction. thats the same as 3*12=36 inches in each direction. now you can find cubic inces using those dimensions instead

- anonymous

so 1177.5*3^3

- anonymous

wait a second. your cyl you have in inch form and your gallons is in feet form. are you going to do your comparison in feet or inches because we need them both in the same format first

- anonymous

ft

- anonymous

so we need to divide 1177.5 in cubed by 12 inches cubed, that gets us feet

- anonymous

oh! heres an idea that one of my teaches tried with us years ago, maybe that will help you with conversions, you can use it for any conversion you want

- anonymous

ok

- anonymous

well apparently i have no idea how to use the equations thinger on this site, so thats not going to work. basically you just need to know how many units to convert and then write out equivalent fractions and then cross out matching units that cancel out.

- anonymous

huh?

- anonymous

http://www.purplemath.com/modules/units.htm

- anonymous

i give up onthis one

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