Question

Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 12 feet by 12 feet by 6 inches for a patio if the concrete costs $64.00 per cubic yard.

Answer 1

wat process

Answer 2

What do you mean?

Answer 3

well are u on flvs

Answer 4

sorry cant help

Answer 5

How much is 12 feet when converted to yards?
How much is 6 inches when converted to yards?

What is the volume of a slab that is 12 feet by 12 feet by 6 inches (except use the measurements you obtained in yards), if the volume of a slab is given by \[V = l*w*h\]where \(l\) is length, \(w\) is width, and \(h\) is height?

Now, if each one of those cubic yards

Answer 6

Now, if each one of those cubic yards costs $64.00, how much do you have to pay for the whole thing?

Answer 7

I'm confused now. What do I do when I convert the feet to yards?

Answer 8

How do you convert inches to yards?

Answer 9

How many feet in 1 yard?

Answer 10

3. But 6 inches isn't even one foot.

Answer 11

Yes, that's right, so it's a fraction of 1 foot, and an even smaller fraction of 1 yard.

Answer 12

\[1 \text{ yard} = 3 \text{ feet}\]Here's my method for error-free unit conversions. Write the equivalence as I did above. Next, change that to a fraction we can multiply or divide by as needed. We have feet and want yards, so we need a fraction that is yards/feet. Divide both sides by \(3 \text{ feet}\) to get
\[\frac{1 \text{ yard}}{3 \text{ feet}} = \frac{3\cancel{\text{ feet}}}{3 \cancel{\text{ feet}}} = 1\]We can multiply or divide by 1 without changing the equation at all, right? If we have a quantity in feet, and we want to convert it to yards, we multiply by \[\frac{1 \text{ yard}}{3\text{ feet}}\]

\[12 \cancel{\text{ feet}}*\frac{1 \text{ yard}}{3 \cancel{\text{ feet}}} = \frac{12*1}{3}\text{ yards} = 4\text{ yards}\]

If you make sure the units cancel correctly, you know you haven't applied a conversion in the wrong direction. If you just multiply or divide by 3, you have no safety check. If we ended up with a unit like \[\frac{\text{feet}^2}{\text{yard}}\]that would be our clue that we did it wrong.

Answer 13

So, our slab is 4 yards by 4 yards by 6 inches. We still need to convert 6 inches to yards. We can do that by using our existing fraction, plus a new one:

\[12 \text{ inches} = 1 \text{ foot}\]We want to convert inches to feet, so we divide both sides by 12 inches to get\[\frac{12 \text{ inches}}{12 \text{ inches}} = \frac{1 \text{ foot}}{12 \text{ inches}} \]

\[6 \text{ inches}*\frac{1\text{ foot}}{12 \text{ inches}}*\frac{1\text{ yard}}{3 \text{ feet}} =6 \cancel{\text{ inches}}*\frac{1\cancel{\text{ foot}}}{12 \cancel{\text{ inches}}}*\frac{1\text{ yard}}{3 \cancel{\text{ feet}}} \]\[=\frac{6}{12*3}\text{ yard} = \frac{1}{6}\text{ yard}\]

Our slab, measured in yards, is 4 yards by 4 yards by 1/6 yard.

Answer 14

What is the volume of the slab? What is the price of the concrete required to make it?

Answer 15

How would I find out the volume? But the price is $64.

Answer 16

Go read my first post, where I tell you how to calculate the volume of the slab.

Not the price per yard, the total price of all of the yards of concrete you will have to buy.

Answer 17

Thank you. I got so confused with the decimal part. You really helped! :) Thanks(:

Answer 18

What's the final answer for the volume of the slab, and the cost of the concrete to make it?

Answer 19

2.66 yards ^3

$170.67

Answer 20

That's what I get as well. Good job!

Answer 21

You could also have done this by converting the price per cubic yard to be the price per cubic foot, or the price per cubic inch, depending on which unit you choose as the common unit for finding the volume. Works out to the same answer so long as you don't make any mistakes! For example, if we converted everything to inches, we'd get 124,416 cubic inches as our volume, and 1 cubic yard is 36*36*36 = 46,656 cubic inches, and 124416/46656 = 8/3 cubic yards, just like you got (8/3 = 2.666666 with the 6 continuing).

Two step formula for success on this problem
1) convert to consistent units
2) don't screw up #1 :-)