Question 1095236
<br>Think of the original pile of sand and the final pile as similar cones.<br>
By a powerful general principle regarding similar figures, the ratio of the volumes of the two cones will be the cube of the scale factor between the two cones (ratio of measures of length).<br>
So the ratio of the heights of the two cones (a measurement of length) will be the cube root of the ratio of their volumes.<br>
Volume of original pile:
{{{V1 = (1/3)(pi)(6^2)(8)}}}
Volume of final pile:
{{{V2 = (1/3)(pi)(6^2)(8) + 200}}}
Ratio of volumes:
{{{V2/V1}}}
Ratio of heights:
{{{(V2/V1)^(1/3)}}}
Height of the final pile:
{{{8*(V2/V1)^(1/3)}}}<br>
By my calculations, the new height is 13.66 feet.