A 44 m long drainage ditch is to be dug. The ditch is to be 1.6 m deep
and 2.4 m wide at the bottom and 3.4 m wide at the top. The two ends
of the trench will be shored and need not be sloped. Calculate the
volume of soil in m3 to be excavated
2007-07-27 20:23:14 · 8 answers · asked by layc_510 2 in Science & Mathematics ➔ Mathematics
End is a trapezium of area , A , say.
A = (1/2)(2.4 + 3.4) (1.6) m ²
A = 4.64 m ²
V = 4.64 x 44 m ³
V = 204 m ³ (to nearest whole number)
2007-07-27 21:16:43 · answer #1 · answered by Como 7 · 0⤊ 0⤋
The cross section of the ditch is a trapezoid so we need to first find the area of the trapezoid.
The formula for this is 1/2 height x lengths of the top and bottom added together.
1/2 (1.6m) x (2.4 +3.4) = 4.64 square meters
For the volume we need to multiply the area times the length of the ditch
4.64 square meters x 44 meters = 204.16 cubic meters
2007-07-28 03:43:35 · answer #2 · answered by kale_ewart 5 · 0⤊ 0⤋
what do you mean by wide at the bottom, and wide at the top?
in this example, i'll assume that this ditch is not a box shape, and you have some obscure triangle /rectangle shape where 1 end of the ditch is wider than the other
after saying that, the ditch is actually 2 shapes in 1, a trangle and a rectangle
what is volume? area X depth
so, for the rectangle part. 44m x 2.4m = area of the rectangle known as A
the trangle part (3.4m - 2.4m = the leftover piece that protrudes out, draw it to see why I did this) = 1
(1m x 44m ) / 2 = the area of the triangle T
A x 1.6m + T x 1.6m = the total volume of the ditch.
easy-as-trangle-shaped desserts!
2007-07-28 03:39:54 · answer #3 · answered by (+_+) B 4 · 0⤊ 1⤋
The ditch is in the shape of a prism.
Volume of a prism = Cross-sectional area * height.
In this case, the "height' is the length of the ditch = 44m
Cross Sectional Area:
The cross-section is clearly a trapezoid.
Area of a trapezoid = 1/2(a+b)h
= (1/2)(2.4 + 3.4)*1.6
= 2.6 * 1.6
= 4.64m^2
Volume = 4.64m^2 * 44m = 204.16m^3
204.16m^3 of soil needs to be excavated.
2007-07-28 03:35:30 · answer #4 · answered by gudspeling 7 · 0⤊ 0⤋
Your ditch is 44m, 1.6m deep. It's 2.4m at the bottom and 3.4m wide at the top.
You can simply compute and average width of the ditch. 2.4m + 3.4m = 5.8m. Average is 2.9m
So, your volume is 44m * 1.6m * 2.9M = 204.16m
2007-07-28 03:33:14 · answer #5 · answered by Joan S 2 · 1⤊ 0⤋
This sounds very much like the volume of a trapezoid.
Check out :
http://mathforum.org/library/drmath/view/56480.html
2007-07-28 03:37:50 · answer #6 · answered by BIGDAWG 4 · 0⤊ 0⤋
My calculations agree with Joan's.
2007-07-28 03:39:27 · answer #7 · answered by Bethany 7 · 0⤊ 0⤋
V = 44 * ((2.4 * 1.6) + 2 * (((3.4 - 2.4)/2) * 1.6/2) = 204.16 m^3
edit for math error
2007-07-28 03:33:06 · answer #8 · answered by mechnginear 5 · 0⤊ 2⤋