Question #0b699

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Question #0b699

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Answer 1 · 2015-10-19T02:19:07

Use the formula for a prismatoid .

Explanation:

The shape of the ore pile is called a prismatoid.

The long side has a base of 500 ft, but the top narrows down to 440 ft. So the shape of this face (and the opposite side) of the prismatoid is a trapezoid .

Now, the narrow side has a base of 60 ft and forms a triangle with a height of 30 feet.

The four faces (two triangles and two trapezoids) meet at the top of the prismatoid to form a straight line that runs parallel to the 500 ft edges.

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The formula for the volume of a prismatoid is:

$V = \frac{1}{6} [B + (4 M) + b] \cdot h$ $V=1/6[B + (4M) + b]*h$

where,

$B =$ $B=$ the area of the base $= 60 \cdot 500 = 30, 000 f t^{2}$ $=60*500=30,000 ft^2$
$b =$ $b=$ the area of the top $= 0$ $=0$ (since it is a straight line)
$M =$ $M=$ the area of the middle section $= 470 \cdot 30 = 14, 100 f t^{2}$ $=470*30=14,100 ft^2$
$h =$ $h=$ the height $= 30 f t$ $=30 ft^$

[ Note : the middle area (M) forms a cross-section in the shape of a rectangle. The ends with the triangles have a base of 60, so halfway up the triangle the line parallel to the base has length 30 ft . Similarly, the trapezoid has a line parallel to the base and halfway up with length $= \frac{1}{2} (440 + 500) = 470 f t$ $=1/2(440+500)=470ft$ .]

Plugging these all into to volume formula:

$V = \frac{1}{6} [30, 000 + (4 \cdot 14, 100) + 0] \cdot 30 = 432, 000 f t^{2}$ $V=1/6[30,000 + (4*14,100) + 0]*30=432,000ft^2$

Answer in tons :

$= 432, 000 f t^{2} \cdot \frac{110 l b s}{f t^{2}} / ((2000 l b s) = 23, 760$ $=432,000ft^2*(110 lbs)/(ft^2)/((2000 lbs) = 23,760$ tons

Hope that helped

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Question #0b699

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