Question

Question #0b699

Answer 1

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.

The formula for the volume of a prismatoid is:

`V=1/6[B + (4M) + b]*h`

where,

`B=` the area of the base `=60*500=30,000 ft^2`
`b=` the area of the top `=0` (since it is a straight line)
`M=` the area of the middle section `=470*30=14,100 ft^2`
`h=` the height `=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 `=1/2(440+500)=470ft`.]

Plugging these all into to volume formula:

`V=1/6[30,000 + (4*14,100) + 0]*30=432,000ft^2`

Answer in tons :

`=432,000ft^2*(110 lbs)/(ft^2)/((2000 lbs) = 23,760` tons

Hope that helped