Question 3. (2 points for (a)-(b), graded for completeness; 4 points for (c)(d), graded for correctness) Sand washing plants remove impurities from sand to create different types of sand with di'erent properties that can be used for various other applications. For example, sand is needed to make concrete, and using an incorrect type of sand results in lower quality concrete. One kind of sand with many applications is silica sand. For instance, silica sand can be used for water ltration, as a component in glass making, and to make ooring materials and roong tiles. Suppose you visit Mathematical Sand, a sand washing plant, and observe sand falling from a conveyor belt onto the top of a conical pile. (For an example of this in real life, see https: //youtu.be/NrAe2LEBDP4?t=121.) Since you're taking calculus, you are curious about how the sand pile is changing over time. After taking some measurements, you observe that the height of the sand pile is always three-eights of the base diameter, and you discover that sand is failling from the conveyor belt onto the pile at a rate of 10m3 / min. (a) Name at least one assumption this problem is making that is unlikely to always be completely correct in real life. Also indicate an external factor that could cause this assumption to no longer hold. (b) Draw a picture of this scenario and label all important quantities involved. (c) Find an expression for how the radius of the sand pile changes over time. Then nd how fast the radius changes when the radius is 4 meters. It helps to know the volume V of a right circular cone is given by = grzh, where 1' is the radius and h is the height. ((21) How fast is the height of the pile changing when the radius is 4 meters