How much MULCH?

[Guest]

Heres the deal. I'm trying to figure out how many bags of mulch I'll need to fill an area.

The bags of mulch are 2 cubic feet in size

I'm filling an OVAL area with the mulch.

The oval is 30' x 13'.

The mulch is going to be 3" thick

how many bags of mulch will I' need to fill the 30 x 13' OVAL 3" think?

[Guest]

An ellipse with "major semi-axis" of length a and "minor semi-axis" of length b has area [tex]\pi ab[/tex]. Here, a is 30 and b is 13 so the area is [tex]\pi(30)(13)= 390\pi= (390)(3.14)= 1224.6[/tex] square inches. That ellipse is to be filled to a height of 3 inches so the amount of mulch needed is 3(1224.6)= 3673.8 cubic inches. One cubic foot is [tex]12^3= 1728[/tex] cubic inches so 3673.8 cubic inches is [tex]\frac{3673.8}{1728}= 2.13[/tex] cubic feet. I would say that one bag of mulch will do you with just slightly less than 3 inches height. (Precisely, 2 bags is 2(1728)= 3456 cubic inches so [tex]\frac{3456}{1224.6}= 2.8[/tex] inches high rather than 3 inches.)

[Guest]

The original post said the ellipse was 30 feet by 13 feet so the area is 1224.6 square feet, not square inches. The three inch thickness is 1/4 foot so the volume needed is [tex]\frac{1224.6}{4}= 306.15[/tex] cubic feet. That would require [tex]\frac{306.15}{2}= 103.075[/tex] or 104 bags of mulch, not one bag!