Here is a question from my math text: How many cubic yards are there in a room measuring 21 feet long by 18 feet wide by 9 feet high?
I have the answer from the text, but I don't understand part of it. It explains 21ft X 18ft X 9ft = 3402 cubic ft
3402 Cubic feet divided by 27 cubic feet per cubic yard = 126 Cubic yards.
I need more explanation.
2007-04-12 12:53:50 · 13 answers · asked by homer742 3 in Science & Mathematics ➔ Mathematics
You folks are awesome. Thank you all very much.
2007-04-12 13:02:05 · update #1
think of a crate that is 1yard (3 feet on each side)
its volume is 1 cubic yard
but you could put 3*3 1 foot cubed boxes on the bottom and add another two layers
so 1 cubic yard holds 3*3*3 = 27 cubic feet
2007-04-12 12:58:32 · answer #1 · answered by hustolemyname 6 · 0⤊ 0⤋
(I'm using * for multiplication, and / for division)
There are 21 * 18 * 9 cubic feet in the room.
There is 1 cubic yard in the room for every 27 cubic feet in the room.
"For every" means you divide.
Therefore, there are 21 * 18 * 9 / 27 cubic yards in the room.
21 * 18 * 9 / 27 = 126.
Another way to do it:
First convert the feet to yards, then multiply them together.
There are 3 feet in a yard, so the answer is:
21/3 * 18/3 * 9/3 = 126.
Why these two methods are mathematically equivalent:
Since it doesn't matter what order you multiply or divide in, you can use algebra to change this to:
(21*18*9) / (3*3*3)
21*18*9 is the number of cubic feet in the room: 3402.
3*3*3 is how many cubic feet are in 1 cubic yard: 27.
3402 cubic feet / 27 cubic feet per cubic yard = 126 cubic yards.
A little more advanced: Notice, you can treat the units like numbers.
1 * [cubic yards] = 27 * [cubic feet]
Therefore,
1 = 27 * [cubic feet] / [cubic yards]
3402 * [cubic feet] / 1 =
3402 * [cubic feet] / (27 * [cubic feet] / [cubic yards])
3402 * [cubic feet] * [cubic yards] / (27 * [cubic feet]) =
3402 * [cubic yards] / 27 = 126 * [cubic yards]
2007-04-12 13:32:28 · answer #2 · answered by happyjack270 3 · 0⤊ 0⤋
This has to do with unit conversions.
Since there are 3 feet in 1 yard, to get from cubic feet to cubic yards, you would have to cube the ratio of 3 ft to 1 yard as seen below:
21ft * 18ft * 9ft = 3402 cubic ft
3402 cubic ft * (1yard/3 feet)^3 =
3402 cubic ft * (1 cubic yard/ 27 cubic feet) =
126 cubic yards.
2007-04-12 13:00:15 · answer #3 · answered by Anonymous · 0⤊ 0⤋
A cubic yard is 3 feet long, 3 feet wide, and 3 feet tall.
So a cubic yard is 3*3*3 = 27 cubic feet
To find the volume of a rectangular room: multiply length times width times height. That's how they got the 3402 cubic feet.
To change cubic feet to cubic yards:
Set up a proportion to make it clearer to you.
1 cubic yard/ 27 cubic feet = n cubic yards / 3402 cubic feet
3402 = 27 n
126 = n
126 cubic yards
2007-04-12 12:59:45 · answer #4 · answered by ecolink 7 · 0⤊ 0⤋
An easier way to look at it would be to put the measurements into the desired term before you do the math.
21ft = 7 yards
18ft = 6 yards
9ft = 3 yards
7 x 6 x 3 = 126
Picture a cardboard box exactly 1 yard wide, 1 yard long, and 1 yard tall. How many boxes 1 foot by 1 foot by 1 foot could you fit in it? 27, 3 wide, 3 deep, 3 high
2007-04-12 12:59:36 · answer #5 · answered by UNITool 6 · 0⤊ 0⤋
There are 27 cubic feet in a cubic yard. Picture it.
A yard is 3 feet. Therefore a cubic yard is 3 feet high, 3 feet wide, and 3 feet long. 3*3*3=27 cubic feet.
2007-04-12 13:00:45 · answer #6 · answered by fredoniahead 2 · 0⤊ 0⤋
SInce there is 3 feet in one yard, there are 3^3 cubic feet in 1 cubic yard. That's why there are 27 cubic feet in 1 cubic yard. For square feet, 3^2 or 9 sq ft in 1 sq yd.
2007-04-12 12:58:04 · answer #7 · answered by richardwptljc 6 · 0⤊ 0⤋
A yard is three feet. A cubic yard is 3*3*3, or 27.
2007-04-12 12:57:22 · answer #8 · answered by Anonymous · 0⤊ 0⤋
21 ft. = 7 yards
18 ft. = 6 yards
9 ft. = 3 yards.
Volume of the room = 21 ft * 18 ft * 9 ft = 3402 ft^3
Volume of the room = 7 yards * 6 yards * 3 yards = 126 yard^3
Thing is, to change from feet to yards, you divide by 3 since 1 yard = 3 feet. Since volume is the product of three terms, you have to divide by 3 several times [3 times actually]. Dividing by 3 3 different times is the same as dividing by 27. That's where the dividing by 27 comes from.
2007-04-12 13:01:41 · answer #9 · answered by seth4all2003 2 · 0⤊ 0⤋
21 feet x 18 feet x 9 feet = 3402 cubic feet
but 21 feet = 7 yards
and 18 feet = 6 yards
and 9 feet = 3 yards
7yards x 6 yards x 3 yards = 126 cubic yards
The "conversion factor" from cubic yards to cubic feet is 27
because 3x3x3 feet cubed = 1x1x1 yard cubed
2007-04-12 12:58:43 · answer #10 · answered by davidosterberg1 6 · 0⤊ 0⤋