# Question #0b699

##### 1 Answer

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:

where,

[ **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

Plugging these all into to volume formula:

**Answer in tons** :

**tons**

Hope that helped