Volume of SoilDate: 02/16/99 at 09:05:17 From: Amy Atteberry Subject: Volume of soil needed for a trapezoidal bed I am building some planting beds in a trapezoidal shape. The beds will be 8" deep. The dimensions of the trapezoidal bed are 2 x 6 x 4 x 4' by 8". Therefore, I need to be able to calculate how many cubic feet of soil will be needed to fill these beds. I look forward to your reply. Date: 02/16/99 at 12:41:14 From: Doctor Rick Subject: Re: Volume of soil needed for a trapezoidal bed Okay, your 3-dimensional shape might be called a "right prism with a trapezoidal base." Your question might still need more clarification. I am guessing that the dimensions of the trapezoid you give are the lengths of the sides, and in this order: 2 +-----+ 4 / \ 4 / \ +-----------+ 6 and that the 2' and 6' sides are parallel. The formula for the area of a trapezoid is A = (L1 + L2) * H / 2 where L1 and L2 are the lengths of the two parallel sides, and H is the height, that is, the perpendicular distance between the parallel sides. We need to find the height. If you draw a line from the left corner of the 2' side, perpendicular to the 6' side, you get a right triangle with hypotenuse 4' and bottom leg 2'. Using the Pythagorean Theorem, we find that the height (the other side of the triangle) is H = sqrt(4^2 - 2^2) = sqrt(12) = 3.464' Now the area of the trapezoid is A = (2' + 6') * 3.464' / 2 = 13.856 ft^2 To get the volume of the prism, we multiply the area of the base by the height; this time the height is the truly vertical dimension, 8" = 2/3 foot. So the volume is V = A * h = 13.856 ft^2 * 2/3 ft = 9.237 ft^3 That's how many cubic feet of soil you need, if I interpreted your description correctly. If not, perhaps I have given you enough information to figure out the volume yourself. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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