You want a five inch thick layer of topsoil for a new 35 foot by 24 foot garden. The dirt store sells by cubic yard. How many cubic yards of topsoil will you need to order? You can only order a whole number of cubic yards. To begin, we’ll find the volume in cubic feet and then convert the cubic feet to cubic yards. Before we find the volume in cubic feet though, we have to have the dimensions in feet. Notice now here, the height, or the thickness, of the topsoil is in inches. And since one foot is equal to 12 inches, one inch is equal to 1/12 of a foot, which means five inches is equal to 5/12 of a foot. And now to determine the volume in cubic feet, the volume is equal to length times width times height, and therefore, the volume is equal to 24 feet times 35 feet times 5/12 of a foot.
Notice how we have feet, times feet, times feet, which gives us the volume in cubic feet. And now we need to determine 24 times 35 times 5/12, which is equal to 350, but of course, we can check this on the calculator if needed. Notice how the product is 350, giving us a volume of 350 cubic feet. And now let’s convert the cubic feet to cubic yards. But before we do this, let’s determine the conversion from cubic yards to cubic feet. Looking at this cube, notice how the dimensions are one yard, by one yard, by one yard. This is one cubic yard, and since one yard is equal to three feet, we can also label the dimensions three feet, by three feet, by three feet, and therefore in cubic feet, the volume is three feet, times three feet, times three feet, which gives us 27 cubic feet.
So now we know one cubic yard equals 27 cubic feet. Let’s use this to convert 350 cubic feet to cubic yards. Let’s first write 350 cubic feet as a fraction with a denominator of one. And now we will multiply by a unit fraction to convert cubic feet to cubic yards. To form the unit fraction, because we have feet in the numerator and we want cubic feet to simplify out, we must have cubic feet in the denominator of the unit fraction, and cubic yards in the numerator.
And since one cubic yard is equal to 27 cubic feet, the unit fraction is one cubic yard over 27 cubic feet. Because we have cubic feet divided by cubic feet, the units of cubic feet simplify out, leaving us with cubic yards. So now multiplying, notice how we have 350 over 27 cubic yards. Let’s go back to the calculator and determine this quotient. 350 divided by 27 is approximately 12.96. Of course, it’s still cubic yards. But remember, we can only order a whole cubic yards, and if we’re anything over 12 cubic yards, we’ll have to order 13 cubic yards.
You must order 13 cubic yards. So remember, even if this was, let’s say, 12.1 cubic yards, you would still have to order 13 cubic yards, because you can only order a whole number of cubic yards, and if you ordered 12, you wouldn’t have enough. I hope you found this helpful..
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