Question 1199918: Mulch is sold by the cubic yard. To estimate number of cu. yds. needed for a circular bed, determine sq. footage.
Sq. footage = area of circle (pi * r^2).
3.1416 * 10^2 = 314 sq. ft. (10 ft. is example).
Convert sq. ft. to cu. ft.
Depth of mulch in inches.
314 * 4 (depth wanted) = 1256
Divide by 324: 1256 / 324 = 3.876 = 4 cu. yds.
My question: What does the 324 signify?
Note: 324 is used also for a square or rectangular bed (after obtaining sq. footage, multiply by depth of mulch needed, and again / by 324.)
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13196)   (Show Source):
You can put this solution on YOUR website!
Apparently you are following a process defined by the resource you are using....
If you are just interested in getting the answer without understanding why the process works, then okay. But the process is a VERY POOR process for understanding how to calculate the number of cubic yards.
And obviously, with the question you are asking, you do NOT understand why the defined process works. And that is as it should be, because the process is NOT a good one.
The problem is that the defined process uses square feet to find the area of the garden, and inches for the depth of the mulch; and it wants the volume of mulch in cubic yards. Doing calculations with mixed units and then getting the final answer by dividing by the mystery number 324 is NOT good practice.
Once again, if you do gardening for a living and just want a blind process for calculating cubic feet of mulch, then go ahead and us the defined process.
But it is not good mathematical practice.
The division by 324 (for any shape garden) comes from two places.
(1) There are 12 inches in a foot; so when you multiply the area in square feet by the depth in inches, your resulting volume in cubic feet is too large by that factor of 12.
and
(2) There are 3^3 = 27 cubic feet in a cubic yard, so you need to divide the volume in cubic feet by 27 to get the volume in cubic yards.
And 12*27 = 324 -- so the calculation by the defined process is too large by a factor of 324, so the last step in the defined process is to divide your answer in mixed units by 324.
Mathematically a much better process....
(1) area (in square feet) = 3.14(10^2) = 314
(2) volume (in cubic feet) = area (in square feet) times depth (in feet) = 314(4/12) = 314(1/3) = 314/3
(3) volume (in cubic yards) = volume (in cubic feet) divided by 27 (cubic feet per cubic yard) = (314/3)/27 = 314/81 = 3.876
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
A = pi*r^2
A = 3.14*10^2
A = 314 sq ft is the approximate area of the circle with radius 10 ft.
The calculation 314*4 only makes sense if the second "4" is in feet.
Multiplying feet with inches doesn't make sense without a conversion.
More generally, the units need to match up when multiplying dimensions.
(314 sq ft) * (4 ft) = 1256 cubic ft is valid
(314 sq ft) * (4 inches) = 1256 cubic ft is NOT valid
The second equation must be this instead
314 sq ft * (4/12) ft = 104.6666667 cubic ft
Note the division by 12. So we have a 12 in the denominator.
4 inches = 4/12 of a foot = 1/3 of a foot
We'll also have 27 in the denominator due to the steps below
1 yard = 3 feet
(1 yard)^3 = (3 feet)^3
1 cubic yard = 27 cubic feet
Therefore 12*27 = 324 is in the denominator to help correct for the error in the equation 314 sq ft * 4 inches = 1256 cubic ft; and to convert from cubic feet to cubic yards.
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